##### Resource Allocation for Secure Communication Systems: Algorithmic Solvability

H. Boche, R.F. Schaefer, H.V. Poor

IEEE International Workshop on Information Forensics and Security (WIFS) 19456004 (2019).

Medium access control and in particular resource allocation is one of the most important tasks when designing wireless communication systems as it determines the overall performance of a system. For the particular allocation of the available resources it is of crucial importance to know whether or not a channel supports a certain quality-of-service (QoS) requirement. This paper develops a decision framework based on Turing machines and studies the algorithmic decidability of whether or not a QoS requirement is met. Turing machines have no limitations on computational complexity, computing capacity, and storage. They can simulate any given algorithm and therewith characterize the fundamental performance limits for today's digital computers. In this paper, secure communication and identification systems are considered both under channel uncertainty and adversarial attacks. While for perfect channel state information, the question is decidable since the corresponding capacity function is computable, it is shown that the corresponding questions become semidecidable in the case of channel uncertainty and adversarial attacks. This means there exist Turing machines that stop and output the correct answer if and only if a channel supports the given QoS requirement. Interestingly, the opposite question of whether a channel capacity is below a certain threshold is not semidecidable.

##### The Solvability Complexity Index of Sampling-based Hilbert Transform Approximations

H. Boche, V. Pohl

13th International Conference on Sampling Theory and Applications (SampTA) 19451267 (2019).

This paper determines the solvability complexity index (SCI) and a corresponding tower of algorithms for the computational problem of calculating the Hilbert transform of a continuous function with finite energy from its samples. It is shown that the SCI of these algorithms is equal to 2 and that the SCI is independent on whether the calculation is done by linear or by general (i.e. linear and/or non-linear) algorithms.

##### Computability of the Fourier Transform and ZFC

H. Boche, U.J. Mönich

13th International conference on Sampling Theory and Applications (SampTA) 19451289 (2019).

In this paper we study the Fourier transform and the possibility to determine the binary expansion of the values of the Fourier transform in the Zermelo-Fraenkel set theory with the axiom of choice included (ZFC). We construct a computable absolutely integrable bandlimited function with continuous Fourier transform such that ZFC (if arithmetically sound) cannot determine a single binary digit of the binary expansion of the Fourier transform at zero. This result implies that ZFC cannot determine for every precision goal a rational number that approximates the Fourier transform at zero. Further, we discuss connections to Turing computability.

##### Differential Power Analysis Attacks from an Information-Theoretic Perspective

A. Grigorescu, H. Boche

IEEE Information Theory Workshop (ITW) 19352987 (2019).

Differential power analysis (DPA) attacks exploit the variance in power measurements of cryptographic devices to recover secret keys. What can an adversary achieve with power measurements? In this work, information-theoretic tools are used to quantify the amount of sensitive information revealed by a power measurement. It is shown that in order to find a secret key, an adversary needs to try a number of different keys. The number is exponential to the key size and the exponent is given by the key's entropy, conditioned on the power measurement.

##### On the Structure of the Capacity Formula for General Finite State Channels with Applications

H. Boche, R.F. Schaefer, H.V. Poor

IEEE Information Theory Workshop (ITW) 19352971 (2019).

Finite state channels (FSCs) model discrete channels with memory where the channel output depends on the channel input and the actual channel state. The capacity of general FSCs has been established as the limit of a sequence of multi-letter expressions; a corresponding finite-letter characterization is not known to date. In this paper, it is shown that it is indeed not possible to find such a finite-letter entropic characterization for FSCs whose input, output, and state alphabets satisfy |X| ≥2, |Y| ≥2, and |S| ≥q2. Further, the algorithmic computability of the capacity of FSCs is studied. To account for this, the concept of a Turing machine is adopted as it provides fundamental performance limits for today's digital computers. It is shown that the capacity of a FSC is not Banach-Mazur computable and therewith not Turing computable for |X| ≥2, |Y| ≥2, |S| ≥2.

##### Coding for Non-IID Sources and Channels: Entropic Approximations and a Question of Ahlswede

H. Boche, R.F. Schaefer, H.V. Poor

2019 IEEE Information Theory Workshop (ITW) 19352964 (2019).

The theory of Verdú and Han provides a powerful framework to analyze and study general non-independent and identically distributed (non-i.i. d.) sources and channels. Already for simple non-i.i. d. sources and channels, this framework can result in complicated general capacity formulas. Ahlswede asked in his Shannon lecture if these general capacity formulas can be effectively, i.e., algorithmically, computed. In this paper, it is shown that there exist computable non-i.i. d. sources and channels, for which the capacity is a non-computable number. Even worse, it is shown that there are non-i.i. d. sources and channels for which the capacity is a computable number, i.e., the limit of the corresponding sequence of multi-letter capacity expressions is computable, but the convergence of this sequence is not effective. This answers Ahlswede's question in a strong form, since in this case, the multi-letter capacity expressions for these sources and channels cannot be used to approximate the optimal performance algorithmically.

##### Impact of substrate induced band tail states on the electronic and optical properties of MoS2

J. Klein, A. Kerelsky, M. Lorke, M. Florian, F. Sigger, J. Kiemle, M. C. Reuter, T. Taniguchi, K. Watanabe, J. Finley, A. N. Pasupathy, A. Holleitner, F. M. Ross, U. Wurstbauer

Applied Physics Letters 115 (26), 261603 (2019).

Substrate, environment, and lattice imperfections have a strong impact on the local electronic structure and the optical properties of atomically thin transition metal dichalcogenides. We find by a comparative study of MoS2 on SiO2 and hexagonal boron nitride (hBN) using scanning tunneling spectroscopy (STS) measurements that the apparent bandgap of MoS2 on SiO2 is significantly reduced compared to MoS2 on hBN. The bandgap energies as well as the exciton binding energies determined from all-optical measurements are very similar for MoS2 on SiO2 and hBN. This discrepancy is found to be caused by a substantial amount of band tail states near the conduction band edge of MoS2 supported by SiO2. The presence of those states impacts the local density of states in STS measurements and can be linked to a broad red-shifted photoluminescence peak and a higher charge carrier density that are all strongly diminished or even absent using high quality hBN substrates. By taking into account the substrate effects, we obtain a quasiparticle gap that is in excellent agreement with optical absorbance spectra and we deduce an exciton binding energy of about 0.53 eV on SiO2 and 0.44 eV on hBN.

##### Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization

G. De Tomasi, D. Hetterich, P. Sala, F. Pollman

Physical Review B 100 (21), 214313 (2019).

We study the t-V disordered spinless fermionic chain in the strong-coupling regime, t/V -> 0. Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space into exponentially many blocks in system size. Macroscopically, these blocks can be characterized by the number of new degrees of freedom, which we refer to as movers. We focus on two limiting cases: blocks with only one mover and ones with a finite density of movers. The former many-particle block can be exactly mapped to a single-particle Anderson model with correlated disorder in one dimension. As a result, these eigenstates are always localized for any finite amount of disorder. The blocks with a finite density of movers, on the other side, show a many-body localized (MBL) transition that is tuned by the disorder strength. Moreover, we provide numerical evidence that its ergodic phase is diffusive at weak disorder. Approaching the MBL transition, we observe subdiffusive dynamics at finite timescales and find indications that this might be only a transient behavior before crossing over to diffusion.

##### Derivation of the Bogoliubov Time Evolution for a Large Volume Mean-Field Limit

S. Petrat, P. Pickl, A. Soffer

Annales Henri Poincare 21 (2), 461–498 (2019).

The derivation of mean-field limits for quantum systems at zero temperature has attracted many researchers in the last decades. Recent developments are the consideration of pair correlations in the effective description, which lead to a much more precise description of both spectral properties and the dynamics of the Bose gas in the weak coupling limit. While mean-field results typically lead to convergence for the reduced density matrix only, one obtains norm convergence when considering the pair correlations proposed by Bogoliubov in his seminal 1947 paper. In this article, we consider an interacting Bose gas in the case where both the volume and the density of the gas tend to infinity simultaneously. We assume that the coupling constant is such that the self-interaction of the fluctuations is of leading order, which leads to a finite (nonzero) speed of sound in the gas. In our first main result, we show that the difference between the N-body and the Bogoliubov description is small in L2 as the density of the gas tends to infinity and the volume does not grow too fast. This describes the dynamics of delocalized excitations of the order of the volume. In our second main result, we consider an interacting Bose gas near the ground state with a macroscopic localized excitation of order of the density. We prove that the microscopic dynamics of the excitation coming from the N-body Schrödinger equation converges to an effective dynamics which is free evolution with the Bogoliubov dispersion relation. The main technical novelty are estimates for all moments of the number of particles outside the condensate for large volume, and in particular control of the tails of their distribution.

##### Weak crystallization of fluctuating skyrmion textures

J. Kindervater, I. Stasinopoulos, A. Bauer, F. Haslbeck, F. Rucker, A. Chacon, S. Mühlbauer, C. Franz, M. Garst, D. Grundler, C. Pfleiderer

Physical Review X 9 , 41059 (2019).

We report an experimental study of the emergence of nontrivial topological winding and long-range order across the paramagnetic-to-skyrmion lattice transition in the transition metal helimagnet MnSi. Combining measurements of the susceptibility with small-angle neutron scattering, neutron-resonance spin-echo spectroscopy, and all-electrical microwave spectroscopy, we find evidence of skyrmion textures in the paramagnetic state exceeding 103 Å, with lifetimes above several 10−9 s. Our experimental findings establish that the paramagnetic-to-skyrmion lattice transition in MnSi is well described by the Landau soft-mode mechanism of weak crystallization, originally proposed in the context of the liquid-to-crystal transition. As a key aspect of this theoretical model, the modulation vectors of periodic small-amplitude components of the magnetization form triangles that add to zero. In excellent agreement with our experimental findings, these triangles of the modulation vectors entail the presence of the nontrivial topological winding of skyrmions already in the paramagnetic state of MnSi when approaching the skyrmion lattice transition.

##### Spin Transport in a Magnetic Insulator with Zero Effective Damping

T. Wimmer, M. Althammer, L. Liensberger, N. Vlietstra, S. Geprägs, M. Weiler, R. Gross, H. Huebl

Physical Review Letters 123 (25), 257201 (2019).

Applications based on spin currents strongly rely on the control and reduction of their effective damping and their transport properties. We here experimentally observe magnon mediated transport of spin (angular) momentum through a 13.4-nm thin yttrium iron garnet film with full control of the magnetic damping via spin-orbit torque. Above a critical spin-orbit torque, the fully compensated damping manifests itself as an increase of magnon conductivity by almost 2 orders of magnitude. We compare our results to theoretical expectations based on recently predicted current induced magnon condensates and discuss other possible origins of the observed critical behavior.

##### Time-dependent density matrix renormalization group quantum dynamics for realistic chemical systems

X. Xie, Y. Liu, Y. Yao, U. Schollwöck, C. Liu, H. Ma

Journal of Chemical Physics 151 (22), 224101 (2019).

Electronic and/or vibronic coherence has been found by recent ultrafast spectroscopy experiments in many chemical, biological, and material systems. This indicates that there are strong and complicated interactions between electronic states and vibration modes in realistic chemical systems. Therefore, simulations of quantum dynamics with a large number of electronic and vibrational degrees of freedom are highly desirable. Due to the efficient compression and localized representation of quantum states in the matrix-product state (MPS) formulation, time-evolution methods based on the MPS framework, which we summarily refer to as tDMRG (time-dependent density-matrix renormalization group) methods, are considered to be promising candidates to study the quantum dynamics of realistic chemical systems. In this work, we benchmark the performances of four different tDMRG methods, including global Taylor, global Krylov, and local one-site and two-site time-dependent variational principles (1TDVP and 2TDVP), with a comparison to multiconfiguration time-dependent Hartree and experimental results. Two typical chemical systems of internal conversion and singlet fission are investigated: one containing strong and high-order local and nonlocal electron-vibration couplings and the other exhibiting a continuous phonon bath. The comparison shows that the tDMRG methods (particularly, the 2TDVP method) can describe the full quantum dynamics in large chemical systems accurately and efficiently. Several key parameters in the tDMRG calculation including the truncation error threshold, time interval, and ordering of local sites were also investigated to strike the balance between efficiency and accuracy of results.

##### Expressive power of tensor-network factorizations for probabilistic modeling

I. Glasser, R. Sweke, N. Pancotti, J. Eisert, J.I. Cirac

Advances in Neural Information Processing Systems (NIPS 2019) 32, (2019).

Tensor-network techniques have recently proven useful in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions. These factorizations include non-negative tensor-trains/MPS, which are in correspondence with hidden Markov models, and Born machines, which are naturally related to the probabilistic interpretation of quantum circuits. When used to model probability distributions, they exhibit tractable likelihoods and admit efficient learning algorithms. Interestingly, we prove that there exist probability distributions for which there are unbounded separations between the resource requirements of some of these tensor-network factorizations. Of particular interest, using complex instead of real tensors can lead to an arbitrarily large reduction in the number of parameters of the network. Additionally, we introduce locally purified states (LPS), a new factorization inspired by techniques for the simulation of quantum systems, with provably better expressive power than all other representations considered. The ramifications of this result are explored through numerical experiments.

##### The Divergence of all Sampling-based Methods for Calculating the Spectral Factorization

H. Boche, V. Pohl

2019 IEEE 58TH Conference on Decision and Control (CDC) 7714-7720 (2019).

This paper investigates the possibility of approximating the spectral factor of continuous spectral densities with finite Dirichlet energy based on finitely many samples of the spectral densities. It will be shown that there exists no sampling-based method which depends continuously on the samples and which is able to approximate the spectral factor arbitrarily well for all continuous densities of finite energy. Instead, to any sampling-based approximation method there exists a large set of spectral densities so that the approximation method does not converge to the spectral factor for every spectral density in this set as the number of available sampling points is increased. Finally, the paper discusses shortly some consequences of these results. Namely, it mentions implications on the inner-outer factorization, it discusses algorithms which are based on a rational approximation of the spectral density, and it considers the Turing computability of the spectral factor.

##### Matrix product state algorithms for Gaussian fermionic states

N. Schuch, B. Bauer

Physical Review B 100, 245121 (2019).

While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of noninteracting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of interest in their own right but also occur as effective models in numerical methods for interacting systems, such as Hartree-Fock, density functional theory, and many others. Often it is desirable to solve systems of many thousand constituent particles, rendering these simulations computationally costly despite their polynomial scaling. We demonstrate how this scaling can be improved by adapting methods based on matrix product states, which have been enormously successful for low-dimensional interacting quantum systems, to the case of free fermions. Compared to the case of interacting systems, our methods achieve an exponential speedup in the entanglement entropy of the state. We demonstrate their use to solve systems of up to one million sites with an effective matrix product state bond dimension of 1015.

##### Nanoscale mapping of carrier recombination in GaAs-AlGaAs core-multishell nanowires by cathodoluminescence imaging in a scanning transmission electron microscope

M. Müller, F. Bertram, P. Veit, B. Loitsch, J. Winnerl, S. Matich, J. J. Finley, G. Koblmueller, J. Christen

Appl. Phys. Lett. 115, 243102 (2019).

Mapping individual radiative recombination channels at the nanoscale in direct correlation with the underlying crystal structure and composition of III–V semiconductor nanostructures requires unprecedented highly spatially resolved spectroscopy methods. Here, we report on a direct one-by-one correlation between the complex radial structure and the distinct carrier recombination channels of single GaAs-AlGaAs core-multishell nanowire heterostructures using low temperature cathodoluminescence spectroscopy directly performed in a scanning transmission electron microscope. Based on an optimized focused ion beam fabrication of the optically active specimen, we directly visualize the radial luminescence evolution and identify four distinct emission lines, i.e., the near band edge and defect luminescence of the GaAs core (819 nm, 837 nm), the emission of the single embedded GaAs quantum well (QW, 785 nm), and the AlGaAs shell luminescence correlated with alloy fluctuations (650–674 nm). The detailed radial luminescence profiles are anticorrelated between QW luminescence and core emission, illustrating the radial carrier transport of the core-shell system. We inspected in detail the low-temperature capture of excess carriers in the quantum well and barriers.

##### Quantum-confinement enhanced thermoelectric properties in modulation-doped GaAs-AlGaAs core-shell nanowires

S. Fust, A. Faustmann, D. J. Carrad, J. Bissinger, B. Loitsch, M. Döblinger, J. Becker, G. Abstreiter, J. J. Finley, G. Koblmueller

Advanced Materials 32, 1905458 (2019).

Nanowires (NWs) hold great potential in advanced thermoelectrics due to their reduced dimensions and low-dimensional electronic character. However, unfavorable links between electrical and thermal conductivity in state-of-the-art unpassivated NWs have, so far, prevented the full exploitation of their distinct advantages. A promising model system for a surface-passivated one-dimensional (1D)-quantum confined NW thermoelectric is developed that enables simultaneously the observation of enhanced thermopower via quantum oscillations in the thermoelectric transport and a strong reduction in thermal conductivity induced by the core–shell heterostructure. High-mobility modulation-doped GaAs/AlGaAs core–shell NWs with thin (sub-40 nm) GaAs NW core channel are employed, where the electrical and thermoelectric transport is characterized on the same exact 1D-channel. 1D-sub-band transport at low temperature is verified by a discrete stepwise increase in the conductance, which coincided with strong oscillations in the corresponding Seebeck voltage that decay with increasing sub-band number. Peak Seebeck coefficients as high as ≈65–85 µV K−1 are observed for the lowest sub-bands, resulting in equivalent thermopower of S2σ ≈ 60 µW m−1 K−2 and S2G ≈ 0.06 pW K−2 within a single sub-band. Remarkably, these core–shell NW heterostructures also exhibit thermal conductivities as low as ≈3 W m−1 K−1, about one order of magnitude lower than state-of-the-art unpassivated GaAs NWs.

##### Solvable lattice models for metals with Z2 topological order

B. Verheijden, Y. Zhao, M. Punk

Scipost Physics 7 (6), 074 (2019).

We present quantum dimer models in two dimensions which realize metallic ground states with Z2 topological order. Our models are generalizations of a dimer model introduced in [PNAS 112, 9552-9557 (2015)] to provide an effective description of unconventional metallic states in hole-doped Mott insulators. We construct exact ground state wave functions in a specific parameter regime and show that the ground state realizes a fractionalized Fermi liquid. Due to the presence of Z2 topological order the Luttinger count is modified and the volume enclosed by the Fermi surface is proportional to the density of doped holes away from half filling. We also comment on possible applications to magic-angle twisted bilayer graphene.

##### Tone Reservation for OFDM With Restricted Carrier Set

H. Boche, U. Mönich

Institute of Electrical and Electronics Engineers (IEEE) Transactions on Information Theory 65 (12), 7935-7949 (2019).

The tone reservation method can be used to reduce the peak to average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) transmission systems. In this paper, the tone reservation method is analyzed for OFDM with a restricted carrier set, where only the positive carrier frequencies are used. Performing a fully analytical analysis, we give a complete characterization of the information sets for which the PAPR problem is solvable. To derive our main result, we connect the PAPR problem with a geometric functional analytic property of certain spaces. Furthermore, we present applications of our theory that give guidelines for choosing the information carriers in the finite setting and discuss a probabilistic approach for selecting the carriers. In addition, it is shown that if there exists an information sequence for which the PAPR problem is not solvable, then the set of information sequences for which the PAPR problem is not solvable is a residual set.

##### Electronic Properties of alpha-RuCl3 in Proximity to Graphene

S. Biswas, Y. Li, S. Winter, J. Knolle, R. Valentí

Physical Review Letters 123 (23), 237201 (2019).

In the pursuit of developing routes to enhance magnetic Kitaev interactions in alpha-RuCl3, as well as probing doping effects, we investigate the electronic properties of alpha-RuCl3 in proximity to graphene. We study alpha-RuCl3/graphene heterostructures via ab initio density functional theory calculations, Wannier projection, and nonperturbative exact diagonalization methods. We show that alpha-RuCl3 becomes strained when placed on graphene and charge transfer occurs between the two layers, making alpha-RuCl3 (graphene) lightly electron doped (hole doped). This gives rise to an insulator-to-metal transition in alpha-RuCl3 with the Fermi energy located close to the bottom of the upper Hubbard band of the t(2g) manifold. These results suggest the possibility of realizing metallic and even exotic superconducting states. Moreover, we show that in the strained alpha-RuCl3 monolayer the Kitaev interactions are enhanced by more than 50% compared to the unstrained bulk structure. Finally, we discuss scenarios related to transport experiments in alpha-RuCl3/graphene heterostructures.

##### Time-evolution methods for matrix-product states

S. Packel, T. Kohler, A. Swoboda, S. Manmana, U. Schollwock, C. Hubig.

Annals of Physics 411, 167998 (2019).

Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W-I,W-II method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

##### Unitary dilations of discrete-time quantum-dynamical semigroups

F. vom Ende, G. Dirr

Journal of Mathematical Physics 60 (12), 122702 (2019).

We show that the discrete-time evolution of an open quantum system generated by a single quantum channel T can be embedded in the discrete-time evolution of an enlarged closed quantum system, i.e., we construct a unitary dilation of the discrete-time quantum-dynamical semigroup (????)??∈ℕ0. In the case of a cyclic channel T, the auxiliary space may be chosen (partially) finite-dimensional. We further investigate discrete-time quantum control systems generated by finitely many commuting quantum channels and prove a similar unitary dilation result as in the case of a single channel.

##### Time-evolution methods for matrix-product states

S. Paeckel, T. Köhler, A. Swoboda, S.R. Manmana, U. Schollwöck, C. Hubig

Annals of Physics 411, 167998 (2019).

Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

##### A Mean Field Limit for the Hamiltonian Vlasov System

R. Neiss, P. Pickl

Journal of Statistical Physics 178 (2), 472–498 (2019).

The derivation of effective equations for interacting many body systems has seen a lot of progress in the recent years. While dealing with classical systems, singular potentials are quite challenging (Hauray and Jabin in Annales scientifiques de l’École Normale Supérieure, 2013, Lazarovici and Pickl in Arch Ration Mech Anal 225(3):1201–1231, 2017) comparably strong results are known to hold for quantum systems (Knowles and Pickl in Comm Math Phys 298:101–139, 2010). In this paper, we wish to show how techniques developed for the derivation of effective descriptions of quantum systems can be used for classical ones. While our future goal is to use these ideas to treat singularities in the interaction, the focus here is to present how quantum mechanical techniques can be used for a classical system and we restrict ourselves to regular two-body interaction potentials. In particular we compute a mean field limit for the Hamilton Vlasov system in the sense of (Fröhlich et al. in Comm Math Phys 288:1023–1058, 2009; Neiss in Arch Ration Mech Anal. https://doi.org/10.1007/s00205-018-1275-8) that arises from classical dynamics. The structure reveals strong analogy to the Bosonic quantum mechanical ensemble of the many-particle Schrödinger equation and the Hartree equation as its mean field limit (Pickl in arXiv:0808.1178v1, 2008).

##### Phase structure of the (1+1)-dimensional massive Thirring model from matrix product states

M.C. Bañuls, K. Cichy, Y. Kao, D.Lin, Y. Lin, D. Tan

Physical Review D Physical Review D, 94504 (2019).

Employing matrix product states as an ansatz, we study the nonthermal phase structure of the (1 + 1)-dimensional massive Thirring model in the sector of a vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate, and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with the nonzero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behavior, and they serve as an important ingredient for controlling the continuum extrapolation of the model.

##### A Schwarz inequality for complex basis function methods in non-Hermitian quantum chemistry

T.H. Thompson, C. Ochsenfeld, T.C. Jagau

Journal of Chemical Physics 151 (18), 184104 (2019).

A generalization of the Schwarz bound employed to reduce the scaling of quantum-chemical calculations is introduced in the context of non-Hermitian methods employing complex-scaled basis functions. Non-Hermitian methods offer a treatment of molecular metastable states in terms of L-2-integrable wave functions with complex energies, but until now, an efficient upper bound for the resulting electron-repulsion integrals has been unavailable due to the complications from non-Hermiticity. Our newly formulated bound allows us to inexpensively and rigorously estimate the sparsity in the complex-scaled two-electron integral tensor, providing the basis for efficient integral screening procedures. We have incorporated a screening algorithm based on the new Schwarz bound into the state-of-the-art complex basis function integral code by White, Head-Gordon, and McCurdy [J. Chem. Phys. 142, 054103 (2015)]. The effectiveness of the screening is demonstrated through non-Hermitian Hartree-Fock calculations of the static field ionization of the 2-pyridoxine 2-aminopyridine molecular complex. Published under license by AIP Publishing.

##### Using Matrix Product States to Study the Dynamical Large Deviations of Kinetically Constrained Models

M.C. Banuls, J.P. Garrahan

Physical Review Letters 123 (20), 200601 (2019).

Here we demonstrate that tensor network techniques-originally devised for the analysis of quantum many-body problems-are well suited for the detailed study of rare event statistics in kinetically constrained models (KCMs). As concrete examples, we consider the Fredrickson-Andersen and East models, two paradigmatic KCMs relevant to the modeling of glasses. We show how variational matrix product states allow us to numerically approximate-systematically and with high accuracy-the leading eigenstates of the tilted dynamical generators, which encode the large deviation statistics of the dynamics. Via this approach, we can study system sizes beyond what is possible with other methods, allowing us to characterize in detail the finite size scaling of the trajectory-space phase transition of these models, the behavior of spectral gaps, and the spatial structure and "entanglement" properties of dynamical phases. We discuss the broader implications of our results.

##### Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions

M. Jeblick, N. Leopold, P.Pickl

Communications in Mathematical Physics 372 (1), 1–69 (2019).

We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting from an interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.

##### Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information

C. Sünderhauf, L. Piroli, X.L. Qi, N. Schuch, J.I. Cirac

Journal of High Energy Physics 38 (2019).

We consider the Brownian SYK model of N interacting Majorana fermions, with random couplings that are taken to vary independently at each time. We study the out-of-time-ordered correlators (OTOCs) of arbitrary observables and the Rényi-2 tripartite information of the unitary evolution operator, which were proposed as diagnostic tools for quantum chaos and scrambling, respectively. We show that their averaged dynamics can be studied as a quench problem at imaginary times in a model of N qudits, where the Hamiltonian displays site-permutational symmetry. By exploiting a description in terms of bosonic collective modes, we show that for the quantities of interest the dynamics takes place in a subspace of the effective Hilbert space whose dimension grows either linearly or quadratically with N , allowing us to perform numerically exact calculations up to N = 106. We analyze in detail the interesting features of the OTOCs, including their dependence on the chosen observables, and of the tripartite information. We observe explicitly the emergence of a scrambling time t∗∼ ln N controlling the onset of both chaotic and scrambling behavior, after which we characterize the exponential decay of the quantities of interest to the corresponding Haar scrambled values.

##### Identification of emergent constraints and hidden order in frustrated magnets using tensorial kernel methods of machine learning

J. Greitemann, K. Liu, L.D.C. Jaubert, H. Yan, N. Shannon, L. Pollet

Physical Review B 100 (17), 174408 (2019).

Machine-learning techniques have proved successful in identifying ordered phases of matter. However, it remains an open question how far they can contribute to the understanding of phases without broken symmetry, such as spin liquids. Here we demonstrate how a machine-learning approach can automatically learn the intricate phase diagram of a classical frustrated spin model. The method we employ is a support vector machine equipped with a tensorial kernel and a spectral graph analysis which admits its applicability in an effectively unsupervised context. Thanks to the interpretability of the machine we are able to infer, in closed form, both order parameter tensors of phases with broken symmetry, and the local constraints which signal an emergent gauge structure, and so characterize classical spin liquids. The method is applied to the classical XXZ model on the pyrochlore lattice where it distinguishes, among others, between a hidden biaxial spin-nematic phase and several different classical spin liquids. The results are in full agreement with a previous analysis by Taillefumier et al. [Phys. Rev. X 7, 041057 (2017)], but go further by providing a systematic hierarchy between disordered regimes, and establishing the physical relevance of the susceptibilities associated with the local constraints. Our work paves the way for the search of new orders and spin liquids in generic frustrated magnets.

##### Efficient variational approach to dynamics of a spatially extended bosonic Kondo model

Y. Ashida, T. Shi, R. Schmidt, H.R. Sadeghpour, J.I. Cirac, E. Demler

Physical Review A 100 (4), 043618 (2019).

We develop an efficient variational approach to studying dynamics of a localized quantum spin coupled to a bath of mobile spinful bosons. We use parity symmetry to decouple the impurity spin from the environment via a canonical transformation and reduce the problem to a model of the interacting bosonic bath. We describe coherent time evolution of the latter using bosonic Gaussian states as a variational ansatz. We provide full analytical expressions for equations describing variational time evolution that can be applied to study in- and out-of-equilibrium phenomena in a wide class of quantum impurity problems. In the accompanying paper [Ashida et al., Phys. Rev. Lett. 123, 183001 (2019)], we present a concrete application of this general formalism to the analysis of the Rydberg central spin model, in which the spin-1/2 Rydberg impurity undergoes spin-changing collisions in a dense cloud of two-component ultracold bosons. To illustrate new features arising from orbital motion of the bath atoms, we compare our results to the Monte Carlo study of the model with spatially localized bosons in the bath, in which random positions of the atoms give rise to random couplings of the standard central spin model.

##### Quantum Rydberg Central Spin Model

Y. Ashida, T. Shi, R. Schmidt, H.R. Sadeghpour, J.I. Cirac, E. Demler

Physical Review Letters 123 (8), 183001 (2019).

We consider dynamics of a Rydberg impurity in a cloud of ultracold bosonic atoms in which the Rydberg electron undergoes spin-changing collisions with surrounding atoms. This system realizes a new type of quantum impurity problems that compounds essential features of the Kondo model, the Bose polaron, and the central spin model. To capture the interplay of the Rydberg-electron spin dynamics and the orbital motion of atoms, we employ a new variational method that combines an impurity-decoupling transformation with a Gaussian ansatz for the bath particles. We find several unexpected features of this model that are not present in traditional impurity problems, including interaction-induced renormalization of the absorption spectrum that eludes simple explanations from molecular bound states, and long-lasting oscillations of the Rydberg-electron spin. We discuss generalizations of our analysis to other systems in atomic physics and quantum chemistry, where an electron excitation of high orbital quantum number interacts with a spinful quantum bath.

##### Transport of Neutral Optical Excitations Using Electric Fields

O. Cotlet, F. Pientka, R. Schmidt, G. Zarand, E. Demler, A. Imamoglu,

Physical Review X 9, 214505 (2019).

Mobile quantum impurities interacting with a fermionic bath form quasiparticles known as Fermi polarons. We demonstrate that a force applied to the bath particles can generate a drag force of similar magnitude acting on the impurities, realizing a novel, nonperturbative Coulomb drag effect. To prove this, we calculate the fully self-consistent, frequency-dependent transconductivity at zero temperature in the Baym-Kadanoff conserving approximation. We apply our theory to excitons and exciton polaritons interacting with a bath of charge carriers in a doped semiconductor embedded in a microcavity. In external electric and magnetic fields, the drag effect enables electrical control of excitons and may pave the way for the implementation of gauge fields for excitons and polaritons. Moreover, a reciprocal effect may facilitate optical manipulation of electron transport. Our findings establish transport measurements as a novel, powerful tool for probing the many-body physics of mobile quantum impurities.

##### Matrix Product States: Entanglement, Symmetries, and State Transformations

D. Sauerwein, A. Molnar, J.I. Cirac, B. Kraus

Physical Review Letters 123 (7), 170504 (2019).

We analyze entanglement in the family of translationally invariant matrix product states (MPS). We give a criterion to determine when two states can be transformed into each other by local operations with a nonvanishing probability, a central question in entanglement theory. This induces a classification within this family of states, which we explicitly carry out for the simplest, nontrivial MPS. We also characterize all symmetries of translationally invariant MPS, both global and local (inhomogeneous). We illustrate our results with examples of states that are relevant in different physical contexts.

##### Tube algebras, excitations statistics and compactification in gauge models of topological phases

A. Bullivant, C. Delcamp

Journal of High Energy Physics 10, 216 (2019).

We consider lattice Hamiltonian realizations of (d+1)-dimensional Dijkgraaf- Witten theory. In (2+1) d, it is well-known that the Hamiltonian yields point-like excita- tions classified by irreducible representations of the twisted quantum double. This can be confirmed using a tube algebra approach. In this paper, we propose a generalisation of this strategy that is valid in any dimensions. We then apply this generalisation to derive the algebraic structure of loop-like excitations in (3+1) d, namely the twisted quantum triple. The irreducible representations of the twisted quantum triple algebra correspond to the simple loop-like excitations of the model. Similarly to its (2+1) d counterpart, the twisted quantum triple comes equipped with a compatible comultiplication map and an R-matrix that encode the fusion and the braiding statistics of the loop-like excitations, respectively. Moreover, we explain using the language of loop-groupoids how a model defined on a man- ifold that is n-times compactified can be expressed in terms of another model in n-lower dimensions. This can in turn be used to recast higher-dimensional tube algebras in terms of lower dimensional analogues.

##### Probing Trions at Chemically Tailored Trapping Defects

H. Kwon, M. Kim, M. Nutz, N.F. Hartmann, V. Perrin, B. Meany, M.S. Hofmann, C.W. Clark, H. Htoon, S.K. Doorn, A. Högele, Y.H. Wang

ACS Cent. Sci. 5, 1786−1794 (2019).

Trions, charged excitons that are reminiscent of hydrogen and positronium ions, have been intensively studied for energy harvesting, light-emitting diodes, lasing, and quantum computing applications because of their inherent connection with electron spin and dark excitons. However, these quasi-particles are typically present as a minority species at room temperature making it difficult for quantitative experimental measurements. Here, we show that by chemically engineering the well depth of sp3 quantum defects through a series of alkyl functional groups covalently attached to semiconducting carbon nanotube hosts, trions can be efficiently generated and localized at the trapping chemical defects. The exciton-electron binding energy of the trapped trion approaches 119 meV, which more than doubles that of “free” trions in the same host material (54 meV) and other nanoscale systems (2–45 meV). Magnetoluminescence spectroscopy suggests the absence of dark states in the energetic vicinity of trapped trions. Unexpectedly, the trapped trions are approximately 7.3-fold brighter than the brightest previously reported and 16 times as bright as native nanotube excitons, with a photoluminescence lifetime that is more than 100 times larger than that of free trions. These intriguing observations are understood by an efficient conversion of dark excitons to bright trions at the defect sites. This work makes trions synthetically accessible and uncovers the rich photophysics of these tricarrier quasi-particles, which may find broad implications in bioimaging, chemical sensing, energy harvesting, and light emitting in the short-wave infrared.

##### Ferromagnetic Resonance with Magnetic Phase Selectivity by Means of Resonant Elastic X-Ray Scattering on a Chiral Magnet

S. Pollath, A. Aqeel, A. Bauer, C. Luo, H. Ryll, F. Radu, C. Pfleiderer, G. Woltersdorf, C.H. Back

Physical Review Letters 123 (16), 167201 (2019).

Cubic chiral magnets, such as Cu2OSeO3, exhibit a variety of noncollinear spin textures, including a trigonal lattice of spin whirls, the so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at gigahertz frequencies, we probe the ferromagnetic resonance (FMR) modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS FMR, is carried out at distinct positions in reciprocal space, it allows us to distinguish contributions originating from different magnetic states, providing information on the precise character, weight, and mode mixing as a prerequisite of tailored excitations for applications.

##### Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux attachment to Z2 lattice gauge theories

L. Barbiero, C. Schweizer, M. Aidelsburger, E. Demler, N. Goldman and F. Grusdt.

Science Advances 5 (10), (2019).

From the standard model of particle physics to strongly correlated electrons, various physical settings are formulated in terms of matter coupled to gauge fields. Quantum simulations based on ultracold atoms in optical lattices provide a promising avenue to study these complex systems and unravel the underlying many-body physics. Here, we demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices, using a combination of coherent lattice modulation with strong interactions. Specifically, we propose implementation of Z2 lattice gauge theories coupled to matter, reminiscent of theories previously introduced in high-temperature superconductivity. We discuss a range of settings from zero-dimensional toy models to ladders featuring transitions in the gauge sector to extended two-dimensional systems. Mastering lattice gauge theories in optical lattices constitutes a new route toward the realization of strongly correlated systems, with properties dictated by an interplay of dynamical matter and gauge fields.

##### Dissipative correlated dynamics of a moving bosonic impurity immersed in a Bose-Einstein Condensate

S. I. Mistakidis, F. Grusdt, G. M. Koutentakis, P. Schmelcher

New Journal of Physics 21, 103026 (2019).

We unravel the nonequilibrium correlated quantum quench dynamics of an impurity traveling through a harmonically confined Bose–Einstein condensate in one-dimension. For weak repulsive interspecies interactions the impurity oscillates within the bosonic gas. At strong repulsions and depending on its prequench position the impurity moves towards an edge of the bosonic medium and subsequently equilibrates. This equilibration being present independently of the initial velocity, the position and the mass of the impurity is inherently related to the generation of entanglement in the many-body system. Focusing on attractive interactions the impurity performs a damped oscillatory motion within the bosonic bath, a behavior that becomes more evident for stronger attractions. To elucidate our understanding of the dynamics an effective potential picture is constructed. The effective mass of the emergent quasiparticle is measured and found to be generically larger than the bare one, especially for strong attractions. In all cases, a transfer of energy from the impurity to the bosonic medium takes place. Finally, by averaging over a sample of simulated in situ single-shot images we expose how the single-particle density distributions and the two-body interspecies correlations can be probed.

##### Analogue quantum chemistry simulation

J. Argüello-Luengo, A. González-Tudela, T. Shi, P. Zoller, I. Cirac.

Nature 574, 215-218 (2019).

Computing the electronic structure of molecules with high precision is a central challenge in the field of quantum chemistry. Despite the success of approximate methods, tackling this problem exactly with conventional computers remains a formidable task. Several theoretical and experimental attempts have been made to use quantum computers to solve chemistry problems, with early proof-of-principle realizations done digitally. An appealing alternative to the digital approach is analogue quantum simulation, which does not require a scalable quantum computer and has already been successfully applied to solve condensed matter physics problems. However, not all available or planned setups can be used for quantum chemistry problems, because it is not known how to engineer the required Coulomb interactions between them. Here we present an analogue approach to the simulation of quantum chemistry problems that relies on the careful combination of two technologies: ultracold atoms in optical lattices and cavity quantum electrodynamics. In the proposed simulator, fermionic atoms hopping in an optical potential play the role of electrons, additional optical potentials provide the nuclear attraction, and a single-spin excitation in a Mott insulator mediates the electronic Coulomb repulsion with the help of a cavity mode. We determine the operational conditions of the simulator and test it using a simple molecule. Our work opens up the possibility of efficiently computing the electronic structures of molecules with analogue quantum simulation.

##### Period-n Discrete Time Crystals and Quasicrystals with Ultracold Bosons

A. Pizzi, J. Knolle, A. Nunnenkamp

Physical Review Letter 123 (15), 150601 (2019).

We investigate the out-of-equilibrium properties of a system of interacting bosons in a ring lattice. We present a Floquet driving that induces clockwise (counterclockwise) circulation of the particles among the odd (even) sites of the ring which can be mapped to a fully connected model of clocks of two counterrotating species. The clocklike motion of the particles is at the core of a period-n discrete time crystal where L = 2n is the number of lattice sites. In the presence of a "staircaselike" on-site potential, we report the emergence of a second characteristic timescale in addition to the period n-tupling. This new timescale depends on the microscopic parameters of the Hamiltonian and is incommensurate with the Floquet period, underpinning a dynamical phase we call "time quasicrystal." The rich dynamical phase diagram also features a thermal phase and an oscillatory phase, all of which we investigate and characterize. Our simple, yet rich model can be realized with state-of-the-art ultracold atoms experiments.

##### Turing Computability of the Fourier Transform of Bandlimited Functions

H. Boche, U.J. Mönich

IEEE International Symposium on Information Theory (ISIT) 19013217 (2019).

The Fourier transform is an essential operation in information sciences. However, it can rarely be calculated in closed form. Nowadays, digital computers are used to compute the Fourier transform. In this paper we study the computability of the Fourier transform. We construct an absolutely integrable bandlimited function that is computable as an element of L 2 , such that its Fourier transform is not Turing computable. This means the Fourier transform is not computable on a digital computer, because we have no way of effectively controlling the approximation error. This result has consequences for algorithms that use the Fourier transform of bandlimited function, e.g., the computation of the convolution via a multiplication in the Fourier domain.

##### On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines

H. Boche, V. Pohl

IEEE International Symposium on Information Theory (ISIT) 19013140 (2019).

The spectral factorization is an important operation in many different applications. This paper studies whether the spectral factor of a given computable spectral density can always be computed on an abstract machine (a Turing machine). It is shown that there are computable spectral densities with very comfortable analytic properties (smoothness and finite energy) such that the corresponding spectral factor can not be determined on a Turing machine. As an application, the paper discusses the possibility of calculating the optimal Wiener filter from computable spectral densities.

##### Identification Capacity of Correlation-Assisted Discrete Memoryless Channels: Analytical Properties and Representations

H. Boche, R.F. Schaefer, H.V. Poor

IEEE International Symposium on Information Theory (ISIT) 19013089 (2019).

The problem of identification is considered, in which it is of interest for the receiver to decide only whether a certain message has been sent or not. Identification via correlation-assisted discrete memoryless channels is studied, where the transmitter and the receiver further have access to correlated source observations. Analytical properties and representations of the corresponding identification capacity are studied. In this paper, it is shown that the identification capacity cannot be represented as a maximization of a single-letter (or multi-letter with fixed length) expression of entropic quantities. Further, it is shown that the identification capacity is not Banach-Mazur computable and therewith not Turing computable. Consequently, there is no algorithm that can simulate or compute the identification capacity, even if there are no limitations on computational complexity and computing power.

##### Entanglement production in the dynamical Casimir effect at parametric resonance

I. Romualdo, L. Hackl, N. YokomizoI. Romualdo, L. Hackl, N. Yokomizo

Physical Review D 100 (6), 065022 (2019).

The particles produced from the vacuum in the dynamical Casimir effect are highly entangled. In order to quantify the correlations generated by the process of vacuum decay induced by moving mirrors, we study the entanglement evolution in the dynamical Casimir effect by computing the time-dependent Rényi and von Neumann entanglement entropy analytically in arbitrary dimensions. We consider the system at parametric resonance, where the effect is enhanced. We find that, in (1+1) dimensions, the entropies grow logarithmically for large times, SA(τ)∼12log(τ), while in higher dimensions (n+1) the growth is linear, SA(t)∼λτ, where λ can be identified with the Lyapunov exponent of a classical instability in the system. In (1+1) dimensions, strong interactions among field modes prevent the parametric resonance from manifesting as a Lyapunov instability, leading to a sublinear entropy growth associated with a constant rate of particle production in the resonant mode. Interestingly, the logarithmic growth comes with a prefactor of 1/2 which cannot occur in time-periodic systems with finitely many degrees of freedom and is thus a special property of bosonic field theories.

##### Deterministic Shaping and Reshaping of Single-Photon Temporal Wave Functions

O. Morin, M. Körber, S. Langenfeld, G. Rempe

Physical Review Letters 123, 133602 (2019).

Thorough control of the optical mode of a single photon is essential for quantum information applications. We present a comprehensive experimental and theoretical study of a light-matter interface based on cavity quantum electrodynamics. We identify key parameters like the phases of the involved light fields and demonstrate absolute, flexible, and accurate control of the time-dependent complex-valued wave function of a single photon over several orders of magnitude. This capability will be an important tool for the development of distributed quantum systems with multiple components that interact via photons.

##### Gaussian time-dependent variational principle for the Bose-Hubbard model

T. Guaita, L. Hackl, T. Shi, C. Hubig, E. Demler, J. I. Cirac

Physical Review B 100 (9), 094529 (2019).

We systematically extend Bogoliubov theory beyond the mean-field approximation of the Bose-Hubbard model in the superfluid phase. Our approach is based on the time-dependent variational principle applied to the family of all Gaussian states (i.e., Gaussian TDVP). First, we find the best ground-state approximation within our variational class using imaginary time evolution in 1D, 2D, and 3D. We benchmark our results by comparing to Bogoliubov theory and DMRG in 1D. Second, we compute the approximate one- and two-particle excitation spectrum as eigenvalues of the linearized projected equations of motion (linearized TDVP). We find the gapless Goldstone mode, a continuum of two-particle excitations and a doublon mode. We discuss the relation of the gap between Goldstone mode and two-particle continuum to the excitation energy of the Higgs mode. Third, we compute linear response functions for perturbations describing density variation and lattice modulation and discuss their relations to experiment. Our methods can be applied to any perturbations that are linear or quadratic in creation/annihilation operators. Finally, we provide a comprehensive overview how our results are related to well-known methods, such as traditional Bogoliubov theory and random phase approximation.

##### Floquet approach to Z2 lattice gauge theories with ultracold atoms in optical lattices

C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, N. Goldman, I. Bloch, M. Aidelsburger.

Nature Physics 15, 1168-1173 (2019).

Quantum simulation has the potential to investigate gauge theories in strongly-interacting regimes, which are up to now inaccessible through conventional numerical techniques. Here, we take a first step in this direction by implementing a Floquet-based method for studying Z2 lattice gauge theories using two-component ultracold atoms in a double-well potential. For resonant periodic driving at the on-site interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits Z2 symmetry. We study the dynamics of the system for different initial states and critically contrast the observed evolution with a theoretical analysis of the full time-dependent Hamiltonian of the periodically-driven lattice model. We reveal challenges that arise due to symmetry-breaking terms and outline potential pathways to overcome these limitations. Our results provide important insights for future studies of lattice gauge theories based on Floquet techniques.

##### Entanglement growth after inhomogenous quenches

T. Rakovszky, C.W. von Keyserlingk, F. Pollmann

Physical Review B 100 (12), 125139 (2019).

We study the growth of entanglement in quantum systems with a conserved quantity exhibiting diffusive transport, focusing on how initial inhomogeneities are imprinted on the entropy. We propose a simple effective model, which generalizes the minimal cut picture of Jonay, Huse, and Nahum [arXiv:803.00089] in such a way that the line tension" of the cut depends on the local entropy density. In the case of noisy dynamics, this is described by the Kardar-Parisi-Zhang (KPZ) equation coupled to a diffusing field. We investigate the resulting dynamics and find that initial inhomogeneities of the conserved charge give rise to features in the entanglement profile, whose width and height both grow in time as alpha root t. In particular, for a domain wall quench, diffusion restricts entanglement growth to be S-VN less than or similar to root t. We find that for charge density wave initial states, these features in the entanglement profile are present even after the charge density has equilibrated. Our conclusions are supported by numerical results on random circuits and deterministic spin chains.

##### Magnetization, d-wave superconductivity, and non-Fermi-liquid behavior in a crossover from dispersive to flat bands

P. Kumar, P. Torma, T.I. Vanhala

Physical Review B 100 (12), 125141 (2019).

We explore the effect of inhomogeneity on electronic properties of the two-dimensional Hubbard model on a square lattice using dynamical mean-field theory (DMFT). The inhomogeneity is introduced via modulated lattice hopping such that in the extreme inhomogeneous limit the resulting geometry is a Lieb lattice, which exhibits a flat-band dispersion. The crossover can be observed in the uniform sublattice magnetization which is zero in the homogeneous case and increases with the inhomogeneity. Studying the spatially resolved frequency-dependent local self-energy, we find a crossover from Fermi-liquid to non-Fermi-liquid behavior happening at a moderate value of the inhomogeneity. This emergence of a non-Fermi liquid is concomitant of a quasiflat band. For finite doping the system with small inhomogeneity displays d-wave superconductivity coexisting with incommensurate spin-density order, inferred from the presence of oscillatory DMFT solutions. The d-wave superconductivity gets suppressed for moderate to large inhomogeneity for any finite doping while the incommensurate spin-density order still exists.

##### High spin-wave propagation length consistent with low damping in a metallic ferromagnet

L. Flacke, L. Liensberger, M. Althammer, H. Huebl, S. Geprags, K. Schultheiss, A. Buzdakov, T. Hula, H. Schultheiss, E.R.J. Edwards, H.T. Nembach, J.M. Shaw, R. Gross, M. Weiler

Applied Physics Letters 115 (12), 122402 (2019).

We report ultralow intrinsic magnetic damping in Co25Fe75 heterostructures, reaching the low 10(-4) regime at room temperature. By using a broadband ferromagnetic resonance technique in out-of-plane geometry, we extracted the dynamic magnetic properties of several Co25Fe75-based heterostructures with varying ferromagnetic layer thicknesses. By measuring radiative damping and spin pumping effects, we found the intrinsic damping of a 26 nm thick sample to be alpha 0 less than or similar to 3.18x10-4. Furthermore, using Brillouin light scattering microscopy, we measured spin-wave propagation lengths of up to (21 +/- 1) mu m in a 26 nm thick Co25Fe75 heterostructure at room temperature, which is in excellent agreement with the measured damping.

##### Magnetoelasticity of Co25Fe75 thin films

D. Schwienbacher, M. Pernpeintner, L. Liensberger, E.R.J. Edwards, H.T. Nembach, J.M. Shaw, M. Weiler, R. Gross, H. Huebl

Journal of Applied Physics 126 (10), 103902 (2019).

We investigate the magnetoelastic properties of Co25Fe75 and Co10Fe90 thin films by measuring the mechanical properties of a doubly clamped string resonator covered with multilayer stacks containing these films. For the magnetostrictive constants, we find lambda Co25Fe75=(-20.68 +/- 0.25)x10-6 and lambda Co10Fe90=(-9.80 +/- 0.12)x10-6 at room temperature, in contrast to the positive magnetostriction previously found in bulk CoFe crystals. Co25Fe75 thin films unite low damping and sizable magnetostriction and are thus a prime candidate for micromechanical magnonic applications, such as sensors and hybrid phonon-magnon systems.

##### Exchange-Enhanced Ultrastrong Magnon-Magnon Coupling in a Compensated Ferrimagnet

L. Liensberger, A. Kamra, H. Maier-Flaig, S. Geprags, A. Erb, S.T.B. Goennenwein, R. Gross, W. Belzig, H. Huebl, M. Weiler

Physical Review Letters 123 (11), 117204 (2019).

We experimentally study the spin dynamics in a gadolinium iron garnet single crystal using broadband ferromagnetic resonance. Close to the ferrimagnetic compensation temperature, we observe ultrastrong coupling of clockwise and counterclockwise magnon modes. The magnon-magnon coupling strength reaches almost 40% of the mode frequency and can be tuned by varying the direction of the external magnetic field. We theoretically explain the observed mode coupling as arising from the broken rotational symmetry due to a weak magnetocrystalline anisotropy. The effect of this anisotropy is exchange enhanced around the ferrimagnetic compensation point.

##### Boundary central charge from bulk odd viscosity: Chiral superfluids

O. Golan, C. Hoyos, S. Moroz

Physical Review B 100 (10), 104512 (2019).

We derive a low-energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave vector, contains a dependence on the chiral central charge c of the boundary degrees of freedom, as well as additional nonuniversal contributions. We identify related bulk observables which allow for a bulk measurement of c. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are required. To complement our results, the effective theory is benchmarked against a perturbative computation within a canonical microscopic model.

##### Matrix product states approaches to operator spreading in ergodic quantum systems

K. Hemery, F. Pollmann, D.J. Luitz

Physical Review B 100 (10), 104303 (2019).

We review different matrix-product-state (MPS) approaches to study the spreading of operators in generic nonintegrable quantum systems. As a common ground to all methods, we quantify this spreading by means of the Frobenius norm of the commutator of a spreading operator with a local operator, which is usually referred to as the out-of-time-order correlation (OTOC) function. We compare two approaches based on matrix-product states in the Schrodinger picture: the time-dependent block decimation (TEBD) and the time-dependent variational principle (TDVP), as well as TEBD based on matrix-product operators directly in the Heisenberg picture. The results of all methods are compared to numerically exact results using Krylov space exact time evolution. We find that for the Schrodinger picture, the TDVP algorithm performs better than the TEBD algorithm.

Moreover, the tails of the OTOC are accurately obtained both by TDVP MPS and TEBD MPO. They are in very good agreement with exact results at short times, and appear to be converged in bond dimensions even at longer times. However, the growth and saturation regimes are not well captured by either of the methods.

##### Signatures of information scrambling in the dynamics of the entanglement spectrum

T. Rakovszky, S. Gopalakrishnan, S.A. Parameswaran, F. Pollmann

Physical Review B 100 (12), 125115 (2019).

We examine the time evolution of the entanglement spectrum of a small subsystem of a nonintegrable spin chain following a quench from a product state. We identify signatures in this entanglement spectrum of the distinct dynamical velocities (related to entanglement and operator spreading) that control thermalization. We show that the onset of level repulsion in the entanglement spectrum occurs on different timescales depending on the "entanglement energy," and that this dependence reflects the shape of the operator front. Level repulsion spreads across the entire entanglement spectrum on a timescale that is parametrically shorter than that for full thermalization of the subsystem. This timescale is also close to when the mutual information between individual spins at the ends of the subsystem reaches its maximum. We provide an analytical understanding of this phenomenon and show supporting numerical data for both random unitary circuits and a microscopic Hamiltonian.

##### Detecting subsystem symmetry protected topological order via entanglement entropy

D.T. Stephen, H. Dreyer, M. Iqbal, N. Schuch

Physical Review B 100, 115112 (2019).

Subsystem symmetry protected topological (SSPT) order is a type of quantum order that is protected by symmetries acting on lower-dimensional subsystems of the entire system. In this paper, we show how SSPT order can be characterized and detected by a constant correction to the entanglement area law, similar to the topological entanglement entropy. Focusing on the paradigmatic two-dimensional cluster phase as an example, we use tensor network methods to give an analytic argument that almost all states in the phase exhibit the same correction to the area law, such that this correction may be used to reliably detect the SSPT order of the cluster phase. Based on this idea, we formulate a numerical method that uses tensor networks to extract this correction from ground-state wave functions. We use this method to study the fate of the SSPT order of the cluster state under various external fields and interactions, and find that the correction persists unless a phase transition is crossed, or the subsystem symmetry is explicitly broken. Surprisingly, these results uncover that the SSPT order of the cluster state persists beyond the cluster phase, thanks to a new type of subsystem time-reversal symmetry. Finally, we discuss the correction to the area law found in three-dimensional cluster states on different lattices, indicating rich behavior for general subsystem symmetries.

##### Photon Correlation Spectroscopy of Luminescent Quantum Defects in Carbon Nanotubes

M. Nutz, J. Zhang, M. Kim, H. Kwon, X. Wu, Y. Wang, A. Högele.

Nano Letters 10, 7078–7084 (2019).

Defect-decorated single-wall carbon nanotubes have shown rapid growing potential for imaging, sensing, and the development of room-temperature single-photon sources. The key to the highly nonclassical emission statistics is the discrete energy spectrum of defect-localized excitons. However, variations in defect configurations give rise to distinct spectral bands that may compromise single-photon efficiency and purity in practical devices, and experimentally it has been challenging to study the exciton population distribution among the various defect-specific states. Here, we performed photon correlation spectroscopy on hexyl-decorated single-wall carbon nanotubes to unravel the dynamics and competition between neutral and charged exciton populations. With autocorrelation measurements at the single-tube level, we prove the nonclassical photon emission statistics of defect-specific exciton and trion photoluminescence and identify their mutual exclusiveness in photoemissive events with cross-correlation spectroscopy. Moreover, our study reveals the presence of a dark state with population-shelving time scales between 10 and 100 ns. These new insights will guide further development of chemically tailored carbon nanotube states for quantum photonics applications.

##### Bogoliubov corrections and trace norm convergence for the Hartree dynamics

D. Mitrouskas, S. Petrat, P. Pickl

Reviews in Mathematical Physics 31 (8), 1950024 (2019).

We consider the dynamics of a large number N of nonrelativistic bosons in the mean field limit for a class of interaction potentials that includes Coulomb interaction. In order to describe the fluctuations around the mean field Hartree state, we introduce an auxiliary Hamiltonian on the N-particle space that is similar to the one obtained from Bogoliubov theory. We show convergence of the auxiliary time evolution to the fully interacting dynamics in the norm of the N-particle space. This result allows us to prove several other results: convergence of reduced density matrices in trace norm with optimal rate, convergence in energy trace norm, and convergence to a time evolution obtained from the Bogoliubov Hamiltonian on Fock space with expected optimal rate. We thus extend and quantify several previous results, e.g., by providing the physically important convergence rates, including time-dependent external fields and singular interactions, and allowing for more general initial states, e.g., those that are expected to be ground states of interacting systems.

##### Anisotropic Strain-Induced Soliton Movement Changes Stacking Order and Band Structure of Graphene Multilayers: Implications for Charge Transport

F.R: Geisenhof, F. Winterer, S. Wakolbinger, T.D. Gokus, Y.C. Durmaz, D. Priesack, J. Lenz, F. Keilmann, K. Watanabe, T. Taniguchi, R. Guerrero-Aviles, M. Pelc, A. Ayuela, R.T. Weitz

ACS Applied Nano Materials 2 (9), 6067-6075 (2019).

The crystal structure of solid-state matter greatly affects its electronic properties. For example, in multilayer graphene, precise knowledge of the lateral layer arrangement is crucial, since the most stable configurations, Bernal and rhombohedral stacking, exhibit very different electronic properties. Nevertheless, both stacking orders can coexist within one flake, separated by a strain soliton that can host topologically protected states. Clearly, accessing the transport properties of the two stackings and the soliton is of high interest. However, the stacking orders can transform into one another, and therefore, the seemingly trivial question of how reliable electrical contact can be made to either stacking order can a priori not be answered easily. Here, we show that manufacturing metal contacts to multilayer graphene can move solitons by several ism, unidirectionally enlarging Bernal domains due to arising mechanical strain. Furthermore, we also find that during dry transfer of multilayer graphene onto hexagonal boron nitride, such a transformation can happen. Using density functional theory modeling, we corroborate that anisotropic deformations of the multilayer graphene lattice decrease the rhombohedral stacking stability. Finally, we have devised systematics to avoid soliton movement, and how to reliably realize contacts to both stacking configurations, which will aid to reliably access charge transport in both stacking configurations.

##### Type and Cotype Constants and the Linear Stability of Wigner's Symmetry Theorem

J. Cuesta

Symmetry-Basel 11 (9), 1107 (2019).

We study the relation between almost-symmetries and the geometry of Banach spaces. We show that any almost-linear extension of a transformation that preserves transition probabilities up to an additive error admits an approximation by a linear map, and the quality of the approximation depends on the type and cotype constants of the involved spaces.

##### Reachability in Infinite-Dimensional Unital Open Quantum Systems with Switchable GKS-Lindblad Generators

F. vom Ende, G. Dirr, M. Keyl, T. Schulte-Herbrueggen

Open Systems & Information Dynamics 26 (3), 1950014 (2019).

In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite-dimensional open quantum dynamical systems following a unital Kossakowski-Lindblad master equation extended by controls. More precisely, their time evolution shall be governed by an inevitable potentially unbounded Hamiltonian drift term H-0, finitely many bounded control Hamiltonians H-j allowing for ( at least) piecewise constant control amplitudes u(j) (t) is an element of R plus a bang-bang (i.e., on-off) switchable noise term in Kossakowski-Lindblad form. Generalizing standard majorization results from finite Gamma(V) infinite dimensions, we show that such bilinear quantum control systems allow to approximately reach any target state majorized by the initial one as up to now it only has been known in finite dimensional analogues. The proof of the result is currently limited to the bounded control Hamiltonians H-j and for noise terms Gamma(V) with compact normal V.

##### Turing Meets Shannon: On the Algorithmic Computability of the Capacitites of Secure Communication Systems

R.F. Schaefer, H. Boche, H.V. Poor

20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 18955576 (2019).

This paper presents the recent progress in studying the algorithmic computability of capacity expressions of secure communication systems. Several communication scenarios are discussed and reviewed including the classical wiretap channel, the wiretap channel with an active jammer, and the problem of secret key generation.

##### NetKet: A machine learning toolkit for many-body quantum systems

G. Carleo, K. Choo, D. Hofmann, J.E.T.Smith, T. Westerhout, F. Alet, E.J. Davis, S. Efthymiou, I. Glasser, S.-H. Lin, M. Mauria, G. Mazzola, C.B. Mendl, E. van Nieuwenburg, O. O’Reilly, H. Théveniaut, G. Torlai, F. Vicentini, A. Wietek

SoftwareX 10, 100311 (2019).

We introduce NetKet, a comprehensive open source framework for the study of many-body quantum systems using machine learning techniques. The framework is built around a general and flexible implementation of neural-network quantum states, which are used as a variational ansatz for quantum wavefunctions. NetKet provides algorithms for several key tasks in quantum many-body physics and quantum technology, namely quantum state tomography, supervised learning from wavefunction data, and ground state searches for a wide range of customizable lattice models. Our aim is to provide a common platform for open research and to stimulate the collaborative development of computational methods at the interface of machine learning and many-body physics.

##### Anomalous spin Hall angle of a metallic ferromagnet determined by a multiterminal spin injection/detection device

T. Wimmer, B. Coester, S. Geprags, R. Gross, S.T.B. Goennenwein, H. Huebl, M. Althammer

Applied Physics Letters 115 (9), 092404 (2019).

We report on the determination of the anomalous spin Hall angle in the ferromagnetic metal alloy cobalt-iron (Co25Fe75, CoFe). This is accomplished by measuring the spin injection/detection efficiency in a multiterminal device with nanowires of platinum (Pt) and CoFe deposited onto the magnetic insulator yttrium iron garnet (Y3Fe5O12, YIG). Applying a spin-resistor model to our multiterminal spin transport data, we determine the magnon conductivity in YIG, the spin conductance at the YIG/CoFe interface, and finally the anomalous spin Hall angle of CoFe as a function of its spin diffusion length in a single device. Our experiments clearly reveal a negative anomalous spin Hall angle of the ferromagnetic metal CoFe, but a vanishing ordinary spin Hall angle. This work, therefore, adds new observations to the results reported in Tian et al. [Phys. Rev. B 94, 020403 (2016)] and Das et al. [Phys. Rev. B 96, 220408(R) (2017)] , where the authors found finite contributions of the ordinary spin Hall angle in the ferromagnetic metals Co and Permalloy. Published under license by AIP Publishing.

##### Many-body chaos near a thermal phase transition

A. Schuckert, M. Knap.

SciPost Physics 7, 022 (2019).

We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.

##### Cavity-control of interlayer excitons in van der Waals heterostructures

M. Forg, L. Colombier, R.K. Patel, J. Lindlau, A.D. Mohite, H. Yamaguchi, M.M. Glazov, D. Hunger, A. Hogele

Nature Communications 10, 3697 (2019).

Monolayer transition metal dichalcogenides integrated in optical microcavities host exciton-polaritons as a hallmark of the strong light-matter coupling regime. Analogous concepts for hybrid light-matter systems employing spatially indirect excitons with a permanent electric dipole moment in heterobilayer crystals promise realizations of exciton-polariton gases and condensates with inherent dipolar interactions. Here, we implement cavity-control of interlayer excitons in vertical MoSe2-WSe2 heterostructures. Our experiments demonstrate the Purcell effect for heterobilayer emission in cavity-modified photonic environments, and quantify the light-matter coupling strength of interlayer excitons. The results will facilitate further developments of dipolar exciton-polariton gases and condensates in hybrid cavity - van der Waals heterostructure systems.

##### MIEZE Neutron Spin-Echo Spectroscopy of Strongly Correlated Electron Systems

C. Franz, S. Saubert, A. Wendl, F.X. Haslbeck, O. Soltwedel, J.K. Jochum, L. SPitz, J. Kindervater, A. Bauer, P. Boni, C. Pfleiderer

Journal of the Physical Society of Japan 88 (8), 081002 (2019).

Recent progress in neutron spin-echo spectroscopy by means of longitudinal Modulation of IntEnsity with Zero Effort (MIEZE) is reviewed. Key technical characteristics are summarized which highlight that the parameter range accessible in momentum and energy, as well as its limitations, are extremely well understood and controlled. Typical experimental data comprising quasi-elastic and inelastic scattering are presented, featuring magneto-elastic coupling and crystal field excitations in Ho2Ti2O7, the skyrmion lattice to paramagnetic transition under applied magnetic field in MnSi, ferromagnetic criticality and spin waves in Fe. In addition bench marking studies of the molecular dynamics in H2O are reported. Taken together. the advantages of MIEZE spectroscopy in studies at small and intermediate momentum transfers comprise an exceptionally wide dynamic range of over seven orders of magnitude, the capability to perform straight forward studies on depolarizing samples or under depolarizing sample environments, as well as on incoherently scattering materials.

##### Topological proximity effects in a Haldane graphene bilayer system

P. Cheng, P. W. Klein, K. Plekhanov, K. Sengstock, M. Aidelsburger, C. Weitenberg, and K. Le Hur.

Physical Review B 100, 081107(R) (2019).

We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half filling, resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counterpropagating (protected) edge modes with different velocities. In the strong-coupling limit, the energy spectrum shows flat bands. Therefore we build a perturbation theory and address further the bulk-edge correspondence. We also show the occurrence of a topological insulating phase with Chern number one when only the lowest band is filled. We generalize the effect to Haldane bilayer systems with asymmetric Semenoff masses. Moreover, we propose an alternative definition of the topological invariant on the Bloch sphere.

##### Topological polarons, quasiparticle invariants and their detection in 1D symmetry-protected phases

F. Grusdt, N. Y. Yao, E. A. Demler

Physical Review B 100, 75126 (2019).

In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological Zak phase is directly related to the Zak phase of an elementary quasiparticle excitation in the system. By considering various systems, we establish this connection for a number of different interacting phases including the Su-Schrieffer-Heeger model, p-wave topological superconductors, and the Haldane chain. Crucially, in contrast to the bulk many-body Zak phase associated with the ground state of such systems, the topological invariant associated with quasiparticle excitations (above this ground state) exhibits a more natural route for direct experimental detection. To this end, we build upon recent work [F. Grusdt, et al., Nat. Commun. 7, 11994 (2016)] and demonstrate that mobile quantum impurities can be used, in combination with Ramsey interferometry and Bloch oscillations, to directly measure these quasiparticle topological invariants. Finally, a concrete experimental realization of our protocol for dimerized Mott insulators in ultracold atomic systems is discussed and analyzed.

##### How Much Delocalisation is Needed for an Enhanced Area Law of the Entanglement Entropy?

P. Müller, L. Pastur, R. Schulte

Commun. Math. Phys. 376, 649 – 679 (2019).

We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logarithmically enhanced area law if the Fermi energy coincides with a critical energy of the model where the localisation length diverges.

##### Universal random codes: capacity regions of the compound quantum multiple-access channel with one classical and one quantum sender

H. Boche, G. Janssen, S. Saeedinaeeni

Quantum Information Processing 18 (8), 246 (2019).

We consider the compound memoryless quantum multiple-access channel (QMAC) with two sending terminals. In this model, the transmission is governed by the memoryless extensions of a completely positive and trace preserving map which can be any element of a prescribed set of possible maps. We study a communication scenario, where one of the senders aims for transmission of classical messages, while the other sender sends quantum information. Combining powerful universal random coding results for classical and quantum information transmission over point-to-point channels, we establish universal codes for the mentioned two-sender task. Conversely, we prove that the two-dimensional rate region achievable with these codes is optimal. In consequence, we obtain a multi-letter characterization of the capacity region of each compound QMAC for the considered transmission task.

##### Low-Scaling Self-Consistent Minimization of a Density Matrix Based Random Phase Approximation Method in the Atomic Orbital Space

D. Graf, M. Beuerle, C. Ochsenfeld

Journal of Chemical Theory and Computation 15 (8), 4468-4477 (2019).

An efficient minimization of the random phase approximation (RPA) energy with respect to the one-particle density matrix in the atomic orbital space is presented. The problem of imposing full self-consistency on functionals depending on the potential itself is bypassed by approximating the RPA Hamiltonian on the basis of the well-known Hartree-Fock Hamiltonian making our self-consistent RPA method completely parameter-free. It is shown that the new method not only outperforms post-Kohn-Sham RPA in describing noncovalent interactions but also gives accurate dipole moments demonstrating the high quality of the calculated densities. Furthermore, the main drawback of atomic orbital based methods, in increasing the prefactor as compared to their canonical counterparts, is overcome by introducing Cholesky decomposed projectors allowing the use of large basis sets. Exploiting the locality of atomic and/or Cholesky orbitals enables us to present a self-consistent RPA method which shows asymptotically quadratic scaling opening the door for calculations on large molecular systems.

##### Ultracompact Photodetection in Atomically Thin MoSe2

M. Blauth, G. Vest, S.L. Rosemary, M. Prechtl, O. Hartwig, M. Jurgensen, M. Kaniber, A.V. Stier, J.J. Finley

ACS Photonics 6 (8), 1902-1909 (2019).

Excitons in atomically thin semiconductors interact very strongly with electromagnetic radiation and are necessarily close to a surface. Here, we exploit the deep-subwavelength confinement of surface plasmon polaritons (SPPs) at the edge of a metal-insulator-metal plasmonic waveguide and their proximity of 2D excitons in an adjacent atomically thin semiconductor to build an ultracompact photodetector. When subject to far-field excitation we show that excitons are created throughout the dielectric gap region of our waveguide and converted to free carriers primarily at the anode of our device. In the near-field regime, strongly confined SPPs are launched, routed and detected in a 20 nm narrow region at the interface between the waveguide and the monolayer semiconductor. This leads to an ultracompact active detector region of only similar to 0.03 mu m(2) that absorbs 86% of the propagating energy in the SPP. Due to the electromagnetic character of the SPPs, the spectral response is essentially identical to the far-field regime, exhibiting strong resonances close to the exciton energies. While most of our experiments are performed on monolayer thick MoSe2, the photocurrent-per-layer increases super linearly in multilayer devices due to the suppression of radiative exciton recombination. These results demonstrate an integrated device for nanoscale routing and detection of light with the potential for on-chip integration at technologically relevant, few-nanometer length scales.

##### Are almost-symmetries almost linear?

J. Cuesta, M.M. Wolf

Journal of Mathematical Physics 60 (8), 082101 (2019).

It d-pends. Wigner's symmetry theorem implies that transformations that preserve transition probabilities of pure quantum states are linear maps on the level of density operators. We investigate the stability of this implication. On the one hand, we show that any transformation that preserves transition probabilities up to an additive epsilon in a separable Hilbert space admits a weak linear approximation, i.e., one relative to any fixed observable. This implies the existence of a linear approximation that is 4 epsilon d-close in Hilbert-Schmidt norm, with d the Hilbert space dimension. On the other hand, we prove that a linear approximation that is close in norm and independent of d does not exist in general. To this end, we provide a lower bound that depends logarithmically on d.

##### Polarization plateaus in hexagonal water ice I-h

M. Gohlke, R. Moessner, F. Pollmann

Physical Review B 100 (1), 014206 (2019).

The protons in water ice are subject to so-called ice rules resulting in an extensive ground-state degeneracy. We study how an external electric field reduces this ground-state degeneracy in hexagonal water ice I-h within a minimal model. We observe polarization plateaus when the field is aligned along the [001] and [010] directions. In each case, one plateau occurs at intermediate polarization with reduced but still extensive degeneracy. The remaining ground states can be mapped to dimer models on the honeycomb and the square lattice, respectively. Upon tilting the external field, we observe an order-disorder transition of Kasteleyn type into a plateau at saturated polarization and vanishing entropy. This transition is investigated analytically using the Kasteleyn matrix and numerically using a modified directed-loop Monte Carlo simulation. The protons in both cases exhibit algebraically decaying correlations. Moreover, the features of the static structure factor are discussed.

##### Polarization plateaus in hexagonal water ice Ih

M. Gohlke, R. Moessner, F. Pollmann

Physical Review B 100, 14206 (2019).

The protons in water ice are subject to so-called ice rules resulting in an extensive ground-state degeneracy. We study how an external electric field reduces this ground-state degeneracy in hexagonal water ice Ih within a minimal model. We observe polarization plateaus when the field is aligned along the [001] and [010] directions. In each case, one plateau occurs at intermediate polarization with reduced but still extensive degeneracy. The remaining ground states can be mapped to dimer models on the honeycomb and the square lattice, respectively. Upon tilting the external field, we observe an order-disorder transition of Kasteleyn type into a plateau at saturated polarization and vanishing entropy. This transition is investigated analytically using the Kasteleyn matrix and numerically using a modified directed-loop Monte Carlo simulation. The protons in both cases exhibit algebraically decaying correlations. Moreover, the features of the static structure factor are discussed.

##### Emergent Glassy Dynamics in a Quantum Dimer Model

J. Feldmeier, F. Pollmann, and M. Knap.

Physical Review Letters 123, 040601 (2019).

We consider the quench dynamics of a two-dimensional quantum dimer model and determine the role of its kinematic constraints. We interpret the nonequilibrium dynamics in terms of the underlying equilibrium phase transitions consisting of a Berezinskii-Kosterlitz-Thouless (BKT) transition between a columnar ordered valence bond solid (VBS) and a valence bond liquid (VBL), as well as a first-order transition between a staggered VBS and the VBL. We find that quenches from a columnar VBS are ergodic and both order parameters and spatial correlations quickly relax to their thermal equilibrium. By contrast, the staggered side of the first-order transition does not display thermalization on numerically accessible timescales. Based on the model’s kinematic constraints, we uncover a mechanism of relaxation that rests on emergent, highly detuned multidefect processes in a staggered background, which gives rise to slow, glassy dynamics at low temperatures even in the thermodynamic limit.

##### Probing nonlocal spatial correlations in quantum gases with ultra-long-range Rydberg molecules

J.D. Whalen, S.K. Kanungo, R. Ding, M. Wagner, R. Schmidt, H.R. Sadeghpour, S. Yoshida, J. Burgdörfer, F.B. Dunning, T.C. Killian

Physical Review A 100, 11402 (2019).

We present photoexcitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in bosonic and fermionic quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wave function Rn. By varying the principal quantum number n of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas g(2)(Rn). We demonstrate this with ultracold Sr gases and probe pair-separation length scales in the range Rn=1400–3200 a0, which are on the order of the thermal de Broglie wavelength for temperatures around 1 μK. We observe bunching for a single-component Bose gas of 84Sr and antibunching due to Pauli exclusion at short distances for a polarized Fermi gas of 87Sr, revealing the effects of quantum statistics.

##### String patterns in the doped Hubbard model

C. S. Chiu, G. Ji, A. Bohrdt, M. Xu, M. Knap, E. Demler, F. Grusdt, M. Greiner, D. Greif.

Science 365, 251-256 (2019).

Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly correlated electrons in solids. In this work, we realize the Hubbard Hamiltonian and search for specific patterns within the individual images of many realizations of strongly correlated ultracold fermions in an optical lattice. Upon doping a cold-atom antiferromagnet, we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables. Our results demonstrate the potential for pattern recognition to provide key insights into cold-atom quantum many-body systems.

##### Minimal energy cost of entanglement extraction

L. Hackl, R.H. Jonsson

Quantum 3, 165 (2019).

We compute the minimal energy cost for extracting entanglement from the ground state of a bosonic or fermionic quadratic system. Specifically, we find the minimal energy increase in the system resulting from replacing an entangled pair of modes, sharing entanglement entropy ΔS, by a product state, and we show how to construct modes achieving this minimal energy cost. Thus, we obtain a protocol independent lower bound on the extraction of pure state entanglement from quadratic systems. Due to their generality, our results apply to a large range of physical systems, as we discuss with examples.

##### A Graph-Based Modular Coding Scheme Which Achieves Semantic Security

M. Wiese, H. Boche

IEEE International Symposium on Information Theory (ISIT) 19012818 (2019).

It is investigated how to achieve semantic security for the wiretap channel. A new type of functions called biregular irreducible (BRI) functions, similar to universal hash functions, is introduced. BRI functions provide a universal method of establishing secrecy. It is proved that the known secrecy rates of any discrete and Gaussian wiretap channel are achievable with semantic security by modular wiretap codes constructed from a BRI function and an error-correcting code. A characterization of BRI functions in terms of edge-disjoint biregular graphs on a common vertex set is derived. This is used to study examples of BRI functions and to construct new ones.

##### Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics

B. Bertini, L. Piroli, M. Kormos

Physical Review B 100 (3), 035108 (2019).

The semiclassical approach introduced by Sachdev and collaborators proved to be extremely successful in the study of quantum quenches in massive field theories, both in homogeneous and inhomogeneous settings. While conceptually very simple, this method allows one to obtain analytic predictions for several observables when the density of excitations produced by the quench is small. At the same time, a novel generalized hydrodynamic (GHD) approach, which captures exactly many asymptotic features of the integrable dynamics, has recently been introduced. Interestingly, also this theory has a natural interpretation in terms of semiclassical particles and it is then natural to compare the two approaches. This is the objective of this work: we carry out a systematic comparison between the two methods in the prototypical example of the sine-Gordon field theory. In particular, we study the “bipartitioning protocol” where the two halves of a system initially prepared at different temperatures are joined together and then left to evolve unitarily with the same Hamiltonian. We identify two different limits in which the semiclassical predictions are analytically recovered from GHD: a particular nonrelativistic limit and the low-temperature regime. Interestingly, the transport of topological charge becomes subballistic in these cases. Away from these limits we find that the semiclassical predictions are only approximate and, in contrast to the latter, the transport is always ballistic. This statement seems to hold true even for the so-called “hybrid” semiclassical approach, where finite time DMRG simulations are used to describe the evolution in the internal space.

##### Equivalence of Sobolev Norms Involving Generalized Hardy Operators

R.L. Frank, K. Merz, H. Siedentop

International Mathematics Research Notices 2021, 2284-2303 (2019).

We consider the fractional Schrödinger operator with Hardy potential and critical or subcritical coupling constant. This operator generates a natural scale of homogeneous Sobolev spaces, which we compare with the ordinary homogeneous Sobolev spaces. As a byproduct, we obtain generalized and reversed Hardy inequalities for this operator. Our results extend those obtained recently for ordinary (non-fractional) Schrödinger operators and have an important application in the treatment of large relativistic atoms.

##### Surface pinning and triggered unwinding of skyrmions in a cubic chiral magnet

P. Milde, E. Neuber, A. Bauer, C. Pfleiderer, L.M. Eng

Physical Review B 100, 24408 (2019).

In the cubic chiral magnet Fe1−xCoxSi a metastable state comprising topologically nontrivial spin whirls, so-called skyrmions, may be preserved down to low temperatures by means of field cooling the sample. This metastable skyrmion state is energetically separated from the topologically trivial ground state by a considerable potential barrier, a phenomenon also referred to as topological protection. Using magnetic force microscopy on the surface of a bulk crystal, we show that certain positions are preferentially and reproducibly decorated with metastable skyrmions, indicating that surface pinning plays a crucial role. Increasing the magnetic field allows an increasing number of skyrmions to overcome the potential barrier and hence to transform into the ground state. Most notably, we find that the unwinding of individual skyrmions may be triggered by the magnetic tip sample interaction itself, however, only when its magnetization is aligned parallel to the external field. This implies that the stray field of the tip is key for locally overcoming the topological protection. Both the control of the position of topologically nontrivial states and their creation and annihilation on demand pose important challenges in the context of potential skyrmionic applications.

##### Thermal tensor renormalization group simulations of square-lattice quantum spin models

H. Li, B.B. Chen, Z.Y. Chen, J. von Delft, A.R.A. Weichselbaum, W. Li

Physical Review B 100 (4), 045110 (2019).

In this work, we benchmark the well-controlled and numerically accurate exponential thermal tensor renormalization group (XTRG) in the simulation of interacting spin models in two dimensions. Finite temperature introduces a finite thermal correlation length xi, such that for system sizes L >> xi finite-size calculations actually simulate the thermodynamic limit. In this paper, we focus on the square lattice Heisenberg antiferromagnet (SLH) and quantum Ising models (QIM) on open and cylindrical geometries up to width W = 10. We explore various one-dimensional mapping paths in the matrix product operator (MPO) representation, whose performance is clearly shown to be geometry dependent. We benchmark against quantum Monte Carlo (QMC) data, yet also the series-expansion thermal tensor network results. Thermal properties including the internal energy, specific heat, and spin structure factors, etc. are computed with high precision, obtaining excellent agreement with QMC results. XTRG also allows us to reach remarkably low temperatures. For SLH, we obtain an energy per site u*(g) similar or equal to -0.6694(4) and a spontaneous magnetization m*(S) similar or equal to 0.30(1) already consistent with the ground-state properties, which is obtained from extrapolated low-T thermal data on W <= 8 cylinders and W <= 10 open strips, respectively. We extract an exponential divergence versus T of the structure factor S(M), as well as the correlation length xi, at the ordering wave vector M = (pi, pi), which represents the renormalized classical behavior and can be observed over a narrow but appreciable temperature window, by analyzing the finite-size data by XTRG simulations. For the QIM with a finite-temperature phase transition, we employ several thermal quantities, including the specific heat, Binder ratio, as well as the MPO entanglement to determine the critical temperature T-c.

##### Putative spin-nematic phase in BaCdVO(PO4)(2)

K. Skoulatos, F. Rucker, G.J. Nilsen, A. Bertin, E. Pomjakushina, J. Olliver, A. Schneidewind, R. Georgii, O. Zaharko, L. Keller, C. Ruegg, C. Pfleiderer, B. Schmidt, N. Shannon, A. Kriele, A. Senyshyn, A. Smerald

Physical Review B 100 (1), 014405 (2019).

We report neutron-scattering and ac magnetic susceptibility measurements of the two-dimensional spin-1/2 frustrated magnet BaCdVO(PO4)(2). At temperatures well below T-N approximate to 1 K, we show that only 34% of the spin moment orders in an up-up-down-down stripe structure. Dominant magnetic diffuse scattering and comparison to published muon-spin-rotation measurements indicates that the remaining 66% is fluctuating. This demonstrates the presence of strong frustration, associated with competing ferromagnetic and antiferromagnetic interactions, and points to a subtle ordering mechanism driven by magnon interactions. On applying magnetic field, we find that at T = 0.1 K the magnetic order vanishes at 3.8 T, whereas magnetic saturation is reached only above 4.5 T. We argue that the putative high-field phase is a realization of the long-sought bond-spin-nematic state.

##### Classifying snapshots of the doped Hubbard model with machine learning

A. Bohrdt, C. S. Chiu, G. Ji, M. Xu, D. Greif, M. Greiner, E. Demler, F. Grusdt, M. Knap.

Nature Physics 15, 921-924 (2019).

Quantum gas microscopes for ultracold atoms can provide high-resolution real-space snapshots of complex many-body systems. We implement machine learning to analyse and classify such snapshots of ultracold atoms. Specifically, we compare the data from an experimental realization of the two-dimensional Fermi–Hubbard model to two theoretical approaches: a doped quantum spin liquid state of resonating valence bond type (1,2), and the geometric string theory (3,4), describing a state with hidden spin order. This technique considers all available information without a potential bias towards one particular theory by the choice of an observable and can therefore select the theory that is more predictive in general. Up to intermediate doping values, our algorithm tends to classify experimental snapshots as geometric-string-like, as compared to the doped spin liquid. Our results demonstrate the potential for machine learning in processing the wealth of data obtained through quantum gas microscopy for new physical insights.

##### Optimal control of hybrid optomechanical systems for generating non-classical states of mechanical motion

V. Bergholm, W. Wieczorek, T. Schulte-Herbrueggen, M. Keyl

Quantum Science and Technology 4 (3), 034001 (2019).

Cavity optomechanical systems are one of the leading experimental platforms for controlling mechanical motion in the quantum regime. We exemplify that the control over cavity optomechanical systems greatly increases by coupling the cavity also to a two-level system, thereby creating a hybrid optomechanical system. If the two-level system can be driven largely independently of the cavity, we show that the nonlinearity thus introduced enables us to steer the extended system to non-classical target states of the mechanical oscillator with Wigner functions exhibiting significant negative regions. We illustrate how to use optimal control techniques beyond the linear regime to drive the hybrid system from the near ground state into a Fock target state of the mechanical oscillator. We base our numerical optimization on realistic experimental parameters for exemplifying how optimal control enables the preparation of decidedly non-classical target states, where naive control schemes fail. Our results thus pave the way for applying the toolbox of optimal control in hybrid optomechanical systems for generating non-classical mechanical states.

##### Removing staggered fermionic matter in U(N) and SU(N) lattice gauge theories

E. Zohar, J.I. Cirac

Physical Review D 99 (11), 114511 (2019).

Gauge theories, through the local symmetry which is in their core, exhibit many local constraints, that must be taken care of and addressed in any calculation. In the Hamiltonian picture this is phrased through the Gauss laws, which are local constraints that restrict the physical Hilbert space and relate the matter and gauge degrees of freedom. In this work, we present a way that uses all the Gauss laws in lattice gauge theories with staggered fermions for completely removing the matter degrees of freedom, at the cost of locally extending the interaction range, breaking the symmetry and introducing new local constraints, due to the finiteness of the original local matter spaces.

##### Efficiently solving the dynamics of many-body localized systems at strong disorder

G. De Tomasi, F. Pollmann, M. Heyl

Physical Review B 99 (24), 241114 (2019).

We introduce a method to efficiently study the dynamical properties of many-body localized systems in the regime of strong disorder and weak interactions. Our method reproduces qualitatively and quantitatively the time evolution with a polynomial effort in system size and independent of the desired time scales. We use our method to study quantum information propagation, correlation functions, and temporal fluctuations in one-and two-dimensional many-body localization systems. Moreover, we outline strategies for a further systematic improvement of the accuracy and we point out relations of our method to recent attempts to simulate the time dynamics of quantum many-body systems in classical or artificial neural networks.

##### Efficiently solving the dynamics of many-body localized systems at strong disorder

G. De Tomasi, F. Pollmann, M. Heyl

Physical Review B 99, 241114 (R) (2019).

We introduce a method to efficiently study the dynamical properties of many-body localized systems in the regime of strong disorder and weak interactions. Our method reproduces qualitatively and quantitatively the time evolution with a polynomial effort in system size and independent of the desired time scales. We use our method to study quantum information propagation, correlation functions, and temporal fluctuations in one- and two-dimensional many-body localization systems. Moreover, we outline strategies for a further systematic improvement of the accuracy and we point out relations of our method to recent attempts to simulate the time dynamics of quantum many-body systems in classical or artificial neural networks.

##### Sub-ballistic Growth of Renyi Entropies due to Diffusion

T. Rakovszky, F. Pollmann, C.W. von Keyserlingk

Physical Review Letters 122 (25), 250602 (2019).

We investigate the dynamics of quantum entanglement after a global quench and uncover a qualitative difference between the behavior of the von Neumann entropy and higher Renyi entropies. We argue that the latter generically grow sub-ballistically, as proportional to root t, in systems with diffusive transport. We provide strong evidence for this in both a U(1) symmetric random circuit model and in a paradigmatic nonintegrable spin chain, where energy is the sole conserved quantity. We interpret our results as a consequence of local quantum fluctuations in conserved densities, whose behavior is controlled by diffusion, and use the random circuit model to derive an effective description. We also discuss the late-time behavior of the second Renyi entropy and show that it exhibits hydrodynamic tails with three distinct power laws occurring for different classes of initial states.

##### Dynamical Topological Quantum Phase Transitions in Nonintegrable Models

I. Hagymasi, C. Hubig, O. Legeza, U. Schollwoeck

Physical Review Letters 122 (25), 250601 (2019).

We consider sudden quenches across quantum phase transitions in the S = 1 XXZ model starting from the Haldane phase. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in the rate function for the return probability. In addition, we show that the temporal behavior of the string order parameter is intimately related to the subsequent dynamical phase transitions. We furthermore find that the dynamical quantum phase transitions can be accompanied by enhanced two-site entanglement.

##### Site-selectively generated photon emitters in monolayer MoS2 via local helium ion irradiation

J. Klein, M. Lorke, M. Florian, F. Sigger, J. Wierzbowski, J. Cerne, K. Müller, T. Taniguchi, K. Watanabe, U. Wurstbauer, M. Kaniber, M. Knap, R. Schmidt, J. Finley, A. Holleitner.

Nature Communications 10, Article number: 2755 (2019).

Quantum light sources in solid-state systems are of major interest as a basic ingredient for integrated quantum photonic technologies. The ability to tailor quantum emitters via site-selective defect engineering is essential for realizing scalable architectures. However, a major difficulty is that defects need to be controllably positioned within the material. Here, we overcome this challenge by controllably irradiating monolayer MoS2 using a sub-nm focused helium ion beam to deterministically create defects. Subsequent encapsulation of the ion exposed MoS2 flake with high-quality hBN reveals spectrally narrow emission lines that produce photons in the visible spectral range. Based on ab-initio calculations we interpret these emission lines as stemming from the recombination of highly localized electron–hole complexes at defect states generated by the local helium ion exposure. Our approach to deterministically write optically active defect states in a single transition metal dichalcogenide layer provides a platform for realizing exotic many-body systems, including coupled single-photon sources and interacting exciton lattices that may allow the exploration of Hubbard physics.

##### Secret message transmission over quantum channels under adversarial quantum noise: Secrecy capacity and super-activation

H. Boche, M. Cai, J. Nötzel, C. Deppe.

Journal of Mathematical Physics 60, 062202-1 to 062202-39 (2019).

We determine the secrecy capacities of arbitrarily varying quantum channels (AVQCs). Both secrecy capacities with average error probability and with maximal error probability are derived. Both derivations are based on one common code construction. The code we construct fulfills a stringent secrecy requirement, which is called the strong code concept. As an application of our result for secret message transmission over AVQCs, we determine when the secrecy capacity is a continuous function of the system parameters and completely characterize its discontinuity points both for average error criterion and for maximal error criterion. Furthermore, we prove the phenomenon “superactivation” for secrecy capacities of arbitrarily varying quantum channels, i.e., two quantum channels both with zero secrecy capacity, which, if used together, allow secure transmission with positive capacity. We give therewith an answer to the question “When is the secrecy capacity a continuous function of the system parameters?,” which has been listed as an open problem in quantum information problem page of the Institut für Theoretische Physik (ITP) Hannover. We also discuss the relations between the entanglement distillation capacity, the entanglement generating capacity, and the strong subspace transmission capacity for AVQCs. Ahlswede et al. made in 2013 the conjecture that the entanglement generating capacity of an AVQC is equal to its entanglement generating capacity under shared randomness assisted quantum coding. We demonstrate that the validity of this conjecture implies that the entanglement generating capacity, the entanglement distillation capacity, and the strong subspace transmission capacity of an AVQC are continuous functions of the system parameters. Consequently, under the premise of this conjecture, the secrecy capacities of an AVQC differ significantly from the general quantum capacities.

##### Helical spin texture in a thin film of superfluid 3He

T. Brauner, S. Moroz

Physical Review B 99, 214506 (2019).

We consider a thin film of superfluid 3He under conditions that stabilize the A phase. We show that in the presence of a uniform superflow and an external magnetic field perpendicular to the film, the spin degrees of freedom develop a nonuniform, helical texture. Our prediction is robust and relies solely on Galilei invariance and other symmetries of 3He, which induce a coupling of the orbital and spin degrees of freedom. The length scale of the helical order can be tuned by varying the velocity of the superflow and the magnetic field and may be in reach of near-future experiments.

##### Atomtronics with a spin: Statistics of spin transport and nonequilibrium orthogonality catastrophe in cold quantum gases

J.S. You, R. Schmidt, D.A. Ivanov, M. Knap, and E. Demler.

Physical Review B 99, 214505 (2019).

We propose to investigate the full counting statistics of nonequilibrium spin transport with an ultracold atomic quantum gas. The setup makes use of the spin control available in atomic systems to generate spin transport induced by an impurity atom immersed in a spin-imbalanced two-component Fermi gas. In contrast to solid-state realizations, in ultracold atoms spin relaxation and the decoherence from external sources is largely suppressed. As a consequence, once the spin current is turned off by manipulating the internal spin degrees of freedom of the Fermi system, the nonequilibrium spin population remains constant. Thus one can directly count the number of spins in each reservoir to investigate the full counting statistics of spin flips, which is notoriously challenging in solid-state devices. Moreover, using Ramsey interferometry, the dynamical impurity response can be measured. Since the impurity interacts with a many-body environment that is out of equilibrium, our setup provides a way to realize the nonequilibrium orthogonality catastrophe. Here, even for spin reservoirs initially prepared in a zero-temperature state, the Ramsey response exhibits an exponential decay, which is in contrast to the conventional power-law decay of Anderson's orthogonality catastrophe. By mapping our system to a multistep Fermi sea, we are able to derive analytical expressions for the impurity response at late times. This allows us to reveal an intimate connection of the decay rate of the Ramsey contrast and the full counting statistics of spin flips.

##### Secure quantum remote state preparation of squeezed microwave states

S. Pogorzalek, K. G. Fedorov, M. Xu, A. Parra-Rodriguez, M. Sanz, M. Fischer, E. Xie, K. Inomata, Y. Nakamura, E. Solano, A. Marx, F. Deppe, R. Gross.

Nature Communications 10, 2604 (2019).

Quantum communication protocols based on nonclassical correlations can be more efficient than known classical methods and offer intrinsic security over direct state transfer. In particular, remote state preparation aims at the creation of a desired and known quantum state at a remote location using classical communication and quantum entanglement. We present an experimental realization of deterministic continuous-variable remote state preparation in the microwave regime over a distance of 35 cm. By employing propagating two-mode squeezed microwave states and feedforward, we achieve the remote preparation of squeezed states with up to 1.6 dB of squeezing below the vacuum level. Finally, security of remote state preparation is investigated by using the concept of the one-time pad and measuring the von Neumann entropies. We find nearly identical values for the entropy of the remotely prepared state and the respective conditional entropy given the classically communicated information and, thus, demonstrate close-to-perfect security.

##### Bosonic superfluid on lowest Landau level

S. Moroz, D. T. Son.

Physic Review Letters 122, 235301 (2019).

We develop a low-energy effective field theory of a two-dimensional bosonic superfluid on the lowest Landau level at zero temperature and identify a Berry term that governs the dynamics of coarse-grained superfluid degrees of freedom. For an infinite vortex crystal we compute how the Berry term affects the low-energy spectrum of soft collective Tkachenko oscillations and non-dissipative Hall responses of the particle number current and stress tensor. This term gives rise to a quadratic in momentum term in the Hall conductivity, but does not generate a non-dissipative Hall viscosity.

##### The Atomic Density on the Thomas-Fermi Length Scale for the Chandrasekhar Hamiltonian

K. Merz, H. Siedentop

Reports on Mathematical Physics 83, 387-391 (2019).

We consider a large neutral atom of atomic number Z, modelled by a pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably rescaled one-particle ground state density on the Thomas–Fermi length scale Z−1/3. Using an observation by Fefferman and Seco, we find that the density on this scale converges to the minimizer of the Thomas–Fermi functional of hydrogen as Z → ∞ when Z/c is fixed to a value not exceeding 2/π. This shows that the electron density on the Thomas–Fermi length scale does not exhibit any relativistic effects.

##### Shaped pulses for transient compensation in quantum-limited electron spin resonance spectroscopy

S. Probst, V. Ranjan, Q. Ansel, R. Heeres, B. Albanese, E. Albertinale, D. Vion, D. Esteve, S.J. Glaser, D. Sugny, P. Bertet

Journal of Magnetic Resonance 303, 42-47 (2019).

In high sensitivity inductive electron spin resonance spectroscopy, superconducting microwave resonators with large quality factors are employed. While they enhance the sensitivity, they also distort considerably the shape of the applied rectangular microwave control pulses, which limits the degree of control over the spin ensemble. Here, we employ shaped microwave pulses compensating the signal distortion to drive the spins faster than the resonator bandwidth. This translates into a shorter echo, with enhanced signal-to-noise ratio. The shaped pulses are also useful to minimize the dead-time of our spectrometer, which allows to reduce the wait time between successive drive pulses. (C) 2019 The Authors. Published by Elsevier Inc.

##### Tensor Networks and their use for Lattice Gauge Theories

M.C. Banuls, K. Cichy, J.I. Cirac, K. Jansen, S. Kühn

Proceedings of Science LATTICE2018, 22 (2019).

Tensor Network States are ansaetze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation of real time evolution, have turned them into one of the most promising techniques to study strongly correlated systems.In the realm of Lattice Gauge Theories they can offer an alternative to standard lattice Monte Carlo calculations, which are suited for static properties and regimes where no sign problem appears. The application of Tensor Networks to this kind of problems is a young but rapidly evolving research field. This paper reviews some of the recent progress in this area, and how, using one dimensional models as testbench, some fundamental milestones have been reached that may pave the way to more ambitious goals.

##### Investigation of the 1+1 dimensional Thirring model using the method of matrix product states

M.C. Banuls, K. Cichy, Y.J. Kao, C.J.D. Lin, Y.P. Lin, T.L. Tan

Proceedings of Science LATTICE2018, 229 (2019).

We present preliminary results of a study on the non-thermal phase structure of the (1+1) dimensional massive Thirring model, employing the method of matrix product states. Through investigating the entanglement entropy, the fermion correlators and the chiral condensate, it is found that this approach enables us to observe numerical evidence of a Kosterlitz-Thouless phase transition in the model.

##### Gaussian states for the variational study of (1+1)-dimensional lattice gauge models

P. Sala, T. Shi, S. Kuehn, M.C. Banuls, E. Demler, J.I. Cirac

Proceedings of Science LATTICE2018, 230 (2019).

We introduce a variational ansatz based on Gaussian states for (1+1)-dimensional lattice gauge models. To this end we identify a set of unitary transformations which decouple the gauge degrees of freedom from the matter fields. Using our ansatz, we study static aspects as well as real-time dynamics of string breaking in two (1+1)-dimensional theories, namely QED and two-color QCD. We show that our ansatz captures the relevant features and is in excellent agreement with data from numerical calculations with tensor networks.

##### Avoided quasiparticle decay from strong quantum interactions

R. Verresen, R. Moessner, F. Pollmann.

Nature Physics 15, 750-753 (2019).

Quantum states of matter—such as solids, magnets and topological phases—typically exhibit collective excitations (for example, phonons, magnons and anyons). These involve the motion of many particles in the system, yet, remarkably, act like a single emergent entity—a quasiparticle. Known to be long lived at the lowest energies, quasiparticles are expected to become unstable when encountering the inevitable continuum of many-particle excited states at high energies, where decay is kinematically allowed. Although this is correct for weak interactions, we show that strong interactions generically stabilize quasiparticles by pushing them out of the continuum. This general mechanism is straightforwardly illustrated in an exactly solvable model. Using state-of-the-art numerics, we find it at work in the spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF). This is surprising given the expectation of magnon decay in this paradigmatic frustrated magnet. Turning to existing experimental data, we identify the detailed phenomenology of avoided decay in the TLHAF material Ba3CoSb2O9, and even in liquid helium, one of the earliest instances of quasiparticle decay. Our work unifies various phenomena above the universal low-energy regime in a comprehensive description. This broadens our window of understanding of many-body excitations, and provides a new perspective for controlling and stabilizing quantum matter in the strongly interacting regime.

##### Quantum phases and topological properties of interacting fermions in one-dimensional superlattices

L. Stenzel, A.L.C. Hayward, C. Hubig, U. Schollwöck, F. Heidrich-Meisner.

Physical Review A 99, 053614 (2019).

The realization of artificial gauge fields in ultracold atomic gases has opened up a path towards experimental studies of topological insulators and, as an ultimate goal, topological quantum matter in many-body systems. As an alternative to the direct implementation of two-dimensional lattice Hamiltonians that host the quantum Hall effect and its variants, topological charge-pumping experiments provide an additional avenue towards studying many-body systems. Here, we consider an interacting two-component gas of fermions realizing a family of one-dimensional superlattice Hamiltonians with onsite interactions and a unit cell of three sites, the ground states of which would be visited in an appropriately defined charge pump. First, we investigate the grand canonical quantum phase diagram of individual Hamiltonians, focusing on insulating phases. For a certain commensurate filling, there is a sequence of phase transitions from a band insulator to other insulating phases (related to the physics of ionic Hubbard models) for some members of the manifold of Hamiltonians. Second, we compute the Chern numbers for the whole manifold in a many-body formulation and show that, related to the aforementioned quantum phase transitions, a topological transition results in a change of the value and sign of the Chern number. We provide both an intuitive and a conceptual explanation and argue that these properties could be observed in quantum-gas experiments.

##### Quantum gas microscopy of Rydberg macrodimers

S. Hollerith, J. Zeiher, J. Rui, A. Rubio-Abadal, V. Walther, T. Pohl, D.M. Stamper-Kurn, I. Bloch, C. Gross

Science 364, 664-667 (2019).

A microscopic understanding of molecules is essential for many fields of natural sciences but their tiny size hinders direct optical access to their constituents. Rydberg macrodimers - bound states of two highly-excited Rydberg atoms - feature bond lengths easily exceeding optical wavelengths. Here we report on the direct microscopic observation and detailed characterization of such macrodimers in a gas of ultracold atoms in an optical lattice. The size of about 0.7 micrometers, comparable to the size of small bacteria, matches the diagonal distance of the lattice. By exciting pairs in the initial two-dimensional atom array, we resolve more than 50 vibrational resonances. Using our spatially resolved detection, we observe the macrodimers by correlated atom loss and demonstrate control of the molecular alignment by the choice of the vibrational state. Our results allow for precision testing of Rydberg interaction potentials and establish quantum gas microscopy as a powerful new tool for quantum chemistry.

##### Quantum Zeno effect generalized

T. Möbus, M. Wolf.

Journal of Mathematical Physics 60, 052201 (2019).

The quantum Zeno effect, in its original form, uses frequent projective measurements to freeze the evolution of a quantum system that is initially governed by a fixed Hamiltonian. We generalize this effect simultaneously in three directions by allowing open system dynamics, time-dependent evolution equations and general quantum operations in place of projective measurements. More precisely, we study Markovian master equations with bounded generators whose time dependence is Lipschitz continuous. Under a spectral gap condition on the quantum operation, we show how frequent measurements again freeze the evolution outside an invariant subspace. Inside this space, the evolution is described by a modified master equation.

##### Bounds on the bipartite entanglement entropy for oscillator systems with or without disorder

V. Beaud, J. Sieber and S. Warzel.

Journal of Physics A: Mathematical and Theoretical 52, 235202 (2019).

We give a direct alternative proof of an area law for the entanglement entropy of the ground state of disordered oscillator systems—a result due to Nachtergaele *et al *(2013 *J. Math. Phys.* **54 **042110). Instead of studying the logarithmic negativity, we invoke the explicit formula for the entanglement entropy of Gaussian states to derive the upper bound. We also contrast this area law in the disordered case with divergent lower bounds on the entanglement entropy of the ground state of one-dimensional ordered oscillator chains.

##### Observation of many-body localization in an one-dimensional system with a single-particle mobility edge

T. Kohlert, S. Scherg, X. Li, H.P. Lüschen, S. Das Sarma, I. Bloch, M. Aidelsburger.

Physical Review Letters 122, 170403 (2019).

We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-dimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-André model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential many-body intermediate phase.

##### Finite-temperature properties of interacting bosons on a two-leg flux ladder

M. Buser, F. Heidrich-Meisner, U. Schollwöck

Physical Review A 99, 053601 (2019).

Quasi-one-dimensional lattice systems such as flux ladders with artificial gauge fields host rich quantum-phase diagrams that have attracted great interest. However, so far, most of the work on these systems has concentrated on zero-temperature phases while the corresponding finite-temperature regime remains largely unexplored. The question if and up to which temperature characteristic features of the zero-temperature phases persist is relevant in experimental realizations. We investigate a two-leg ladder lattice in a uniform magnetic field and concentrate our study on chiral edge currents and momentum-distribution functions, which are key observables in ultracold quantum-gas experiments. These quantities are computed for hard-core bosons as well as noninteracting bosons and spinless fermions at zero and finite temperatures. We employ a matrix-product-state based purification approach for the simulation of strongly interacting bosons at finite temperatures and analyze finite-size effects. Our main results concern the vortex-fluid-to-Meissner crossover of strongly interacting bosons. We demonstrate that signatures of the vortex-fluid phase can still be detected at elevated temperatures from characteristic finite-momentum maxima in the momentum-distribution functions, while the vortex-fluid phase leaves weaker fingerprints in the local rung currents and the chiral edge current. In order to determine the range of temperatures over which these signatures can be observed, we introduce a suitable measure for the contrast of these maxima. The results are condensed into a finite-temperature crossover diagram for hard-core bosons.

##### Lower bound on Hartree-Fock Energy of the electron gas

D. Gontier, C. Hainzl, M. Lewin

Physical Review A 99, 052501 (2019).

The Hartree-Fock ground state of a homogeneous electron gas is never translation invariant, even at high densities. As proved by Overhauser, the (paramagnetic) free Fermi gas is always unstable under the formation of spin- or charge-density waves. We give here an explicit bound on the energy gain due to the breaking of translational symmetry. Our bound is exponentially small at high density, which justifies a posteriori the use of the noninteracting Fermi gas as a reference state in the large-density expansion of the correlation energy of the homogeneous electron gas. We are also able to discuss the positive temperature phase diagram and prove that the Overhauser instability only occurs at temperatures which are exponentially small at high density. Our work sheds a new light on the Hartree-Fock phase diagram of the homogeneous electron gas.

##### Incommensurate 2k(F) density wave quantum criticality in two-dimensional metals

J. Halblinger, D. Pimenov, M. Punk

Physical Review B 99 (19), 195102 (2019).

We revisit the problem of two-dimensional metals in the vicinity of a quantum phase transition to incommensurate Q = 2k(F) charge-density-wave order, where the order-parameter wave vector Q connects two hot spots on the Fermi surface with parallel tangents. Earlier theoretical works argued that such critical points are potentially unstable, if the Fermi surface at the hot spots is not sufficiently flat. Here we perform a controlled, perturbative renormalization-group analysis and find a stable fixed point corresponding to a continuous quantum phase transition, which exhibits a strong dynamical nesting of the Fermi surface at the hot spots. We derive scaling forms of correlation functions at the critical point and discuss potential implications for experiments with transition-metal dichalcogenides and rare-earth tellurides.

##### Accidental Contamination of Substrates and Polymer Films by Organic Quantum Emitters

A. Neumann, J. Lindlau, S. Thomas, T. Basche, A. Hoegele

Nano Letters 19 (5), 3207-3213 (2019).

We report the observation of ubiquitous contamination of dielectric substrates and poly(methyl methacrylate) matrices by organic molecules with optical transitions in the visible spectral range. Contamination sites of individual solvent-related fluorophores in thin films of poly(methyl methacrylate) constitute fluorescence hotspots with quantum emission statistics and quantum yields approaching 30% at cryogenic temperatures. Our findings not only resolve prevalent puzzles in the assignment of spectral features to various nanoemitters on bare dielectric substrates or in polymer matrices but also identify the means for the simple and cost-efficient realization of single-photon sources in the visible spectral range.

##### Message Transmission Over Classical Quantum Channels With a Jammer With Side Information: Message Transmission Capacity and Resources

H. Boche, M. Cai, N. Cai.

IEEE Transactions on Information Theory 65 (5), 2922 - 2943 (2019).

In this paper, a new model for arbitrarily varying classical-quantum channels is proposed. In this model, a jammer has side information. The communication scenario in which a jammer can select only classical inputs as a jamming sequence is considered in the first part of the paper. This situation corresponds to the standard model of arbitrarily varying classical-quantum channels. Two scenarios are considered. In the first scenario, the jammer knows the channel input, while in the second scenario the jammer knows both the channel input and the message. The transmitter and receiver share a secret random key with a vanishing key rate. The capacity for both average and maximum error criteria for both scenarios is determined in this paper. A strong converse is also proved. It is shown that all these corresponding capacities are equal, which means that additionally revealing the message to the jammer does not change the capacity. The communication scenario with a fully quantum jammer is considered in the second part of the paper. A single letter characterization for the capacity with secret random key as assistance for both average and maximum error criteria is derived in the paper.

##### Breakdown of corner states and carrier localization by monolayer fluctuations in a radial nanowire quantum wells

M. M. Sonner, A. Sitek, L. Janker, D. Rudolph, D. Ruhstorfer, M. Döblinger, A. Manolescu, G. Abstreiter, J. J. Finley, A. Wixforth, G. Koblmueller, H. J. Krenner

Nano Lett. 19 (5), 3336-3343 (2019).

We report a comprehensive study of the impact of the structural properties in radial GaAs-Al0.3Ga0.7As nanowire-quantum well heterostructures on the optical recombination dynamics and electrical transport properties, emphasizing particularly the role of the commonly observed variations of the quantum well thickness at different facets. Typical thickness fluctuations of the radial quantum well observed by transmission electron microscopy lead to pronounced localization. Our optical data exhibit clear spectral shifts and a multipeak structure of the emission for such asymmetric ring structures resulting from spatially separated, yet interconnected quantum well systems. Charge carrier dynamics induced by a surface acoustic wave are resolved and prove efficient carrier exchange on native, subnanosecond time scales within the heterostructure. Experimental findings are corroborated by theoretical modeling, which unambiguously show that electrons and holes localize on facets where the quantum well is the thickest and that even minute deviations of the perfect hexagonal shape strongly perturb the commonly assumed 6-fold symmetric ground state.

##### Thermal characterization of thin films via dynamic infrared thermography

A. Greppmair, N. Galfe, K. Amend, M. Stutzmann, M.S. Brandt

Review of Scientific Instruments 90, 44903 (2019).

We extend the infrared thermography of thin materials for measurements of the full time response to homogeneous heating via illumination. We demonstrate that the thermal conductivity, the heat capacity, as well as the thermal diffusivity can be determined comparing the experimental data to finite difference simulations using a variety of test materials such as thin doped and undoped silicon wafers, sheets of steel, as well as gold and polymer films. We show how radiative cooling during calibration and measurement can be accounted for and that the effective emissivity of the material investigated can also be measured by the setup developed.

##### Eigenstate thermalization and quantum chaos in the Holstein polaron model

D. Jansen, J. Stolpp, L. Vidmar, and F. Heidrich-Meisner.

Physical Review B 99, 155130 (2019).

The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and single-component systems of spins, fermions, or bosons. The paradigmatic example for thermalization in solid-state physics are phonons serving as a bath for electrons. This situation is often viewed from an open-quantum-system perspective. Here, we ask whether a minimal microscopic model for electron-phonon coupling is quantum chaotic and whether it obeys ETH, if viewed as a closed quantum system. Using exact diagonalization, we address this question in the framework of the Holstein polaron model. Even though the model describes only a single itinerant electron, whose coupling to dispersionless phonons is the only integrability-breaking term, we find that the spectral statistics and the structure of Hamiltonian eigenstates exhibit essential properties of the corresponding random-matrix ensemble. Moreover, we verify the ETH ansatz both for diagonal and off-diagonal matrix elements of typical phonon and electron observables, and show that the ratio of their variances equals the value predicted from random-matrix theory.

##### On the Fourier Representation of Computable Continuous Signals

H. Boche, U.J. Mönich

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 18778530 (2019).

In this paper we study whether it is possible to decide algorithmically if the Fourier series of a continuous function converges uniformly. We show that this decision cannot be made algorithmically, because there exists no Turing machine that can decide for each and every continuous functions whether its Fourier series converges uniformly. Turing computability describes the theoretical feasible that can be implemented on a digital computer, hence the result shows that there exists no algorithm that can perform this decision.

##### On the Computability of the Secret Key Capacity Under Rate Constraints

H. Boche, R.F. Schaefer, H.V. Poor

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 18778155 (2019).

Secret key generation refers to the problem of generating a common secret key without revealing any information about it to an eaves-dropper. All users observe correlated components of a common source and can further use a rate-limited public channel for discussion which is open to eavesdroppers. This paper studies the Turing computability of the secret key capacity with a single rate-limited public forward transmission. Turing computability provides fundamental performance limits for today's digital computers. It is shown that the secret key capacity under rate constraints is not Turing computable, and consequently there is no algorithm that can simulate or compute the secret key capacity, even if there are no limitations on computational complexity and computing power. On the other hand, if there are no rate constraints on the forward transmission, the secret key capacity is Turing computable. This shows that restricting the communication rate over the public channel transforms a Turing computable problem into a non-computable problem. To the best of our knowledge, this is the first time that such a phenomenon has been observed.

##### Detectability of Denial-of-Service Attacks on Communication Systems

H. Boche, R.F. Schaefer, H.V. Poor

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 18778774 (2019).

Wireless communication systems are inherently vulnerable to adversarial attacks since malevolent jammers might jam and disrupt the legitimate transmission intentionally. Accordingly it is of crucial interest for the legitimate users to detect such adversarial attacks. This paper develops a detection framework based on Turing machines and studies the detectability of adversarial attacks. Of particular interest are so-called denial-of-service attacks in which the jammer is able to completely prevent any transmission. It is shown that there exists no Turing machine which can detect such an attack and consequently there is no algorithm that can decide whether or not such a denialof-service attack takes place, even if there are no limitations on computational complexity and computing capacity of the hardware.

##### Analytic Properties of Downsampling for Bandlimited Signals

H. Boche, U.J. Mönich

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 18791617 (2019).

In this paper we study downsampling for bandlimited signals. Downsampling in the discrete-time domain corresponds to a removal of samples. For any downsampled signal that was created from a bandlimited signal with finite energy, we can always compute a bandlimited continuous-time signal such that the samples of this signal, taken at Nyquist rate, are equal to the downsampled discrete-time signal. However, as we show, this is no longer true for the space of bounded bandlimited signals that vanish at infinity. We explicitly construct a signal in this space, which after downsampling does not have a bounded bandlimited interpolation. This shows that downsampling in this signal space is an operation that can lead out of the set of discrete-time signals for which we have a one-to-one correspondence with continuous-time signals.

##### Quantized Conductance in Topological Insulators Revealed by the Shockley-Ramo Theorem

P. Seifert, M. Kundinger, G. Shi, X.Y. He, K.H. Wu, Y.Q. Li, A. Holleitner, C. Kastl

Physical Review Letters 122 (14), 146804 (2019).

Crystals with symmetry-protected topological order, such as topological insulators, promise coherent spin and charge transport phenomena even in the presence of disorder at room temperature. We demonstrate how to image and read out the local conductance of helical surface modes in the prototypical topological insulators Bi2Se3 and BiSbTe3. We apply the so-called Shockley-Ramo theorem to design an optoelectronic probe circuit for the gapless surface states, and we find a well-defined conductance quantization at le(2)/h within the experimental error without any external magnetic field. The unprecedented response is a clear signature of local spin-polarized transport, and it can be switched on and off via an electrostatic field effect. The macroscopic, global readout scheme is based on an electrostatic coupling from the local excitation spot to the readout electrodes, and it does not require coherent transport between electrodes, in contrast to the conventional Landauer-Biittiker description. It provides a generalizable platform for studying further nontrivial gapless systems such as Weyl semimetals and quantum spin-Hall insulators.

##### Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet

L. Chen, D.W. Qu, B.B. Chen, S.S. Gong, J. von Delft, A. Weichselbaum, W. Li

Physical Review B 99 (14), 140404 (2019).

The anomalous thermodynamic properties of the paradigmatic frustrated spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLH) has remained an open topic of research over decades, both experimentally and theoretically. Here, we further the theoretical understanding based on the recently developed, powerful exponential tensor renormalization group method on cylinders and stripes in a quasi-one-dimensional (1D) setup, as well as a tensor product operator approach directly in 2D. The observed thermal properties of the TLH are in excellent agreement with two recent experimental measurements on the virtually ideal TLH material Ba8CoNb6O24. Remarkably, our numerical simulations reveal two crossover temperature scales, at T-l/J similar to 0.20 and T-h/J similar to 0.55, with J the Heisenberg exchange coupling, which are also confirmed by a more careful inspection of the experimental data. We propose that in the intermediate regime between the low-temperature scale T-l and the higher one T-h, the "rotonlike" excitations are activated with a strong chiral component and a large contribution to thermal entropies. Bearing remarkable resemblance to the renowned roton thermodynamics in liquid helium, these gapped excitations suppress the incipient 120 degrees order that emerges for temperatures below T-l.

##### Resonance Fluorescence of GaAs Quantum Dots with Near-Unity Photon Indistinguishability

E. Scholl, L. Hanschke, L. Schweickert, K.D. Zeuner, M. Reindl, S.F.C. da Silva, T. Lettner, R. Trotta, J.J. Finley, K. Müller, A. Rastelli, V. Zwiller, K.D. Jons

Nano Letters 19 (4), 2404-2410 (2019).

Photonic quantum technologies call for scalable quantum light sources that can be integrated, while providing the end user with single and entangled photons on demand. One promising candidate is strain free GaAs/A1GaAs quantum dots obtained by aluminum droplet etching. Such quantum dots exhibit ultra low multi-photon probability and an unprecedented degree of photon pair entanglement. However, different to commonly studied InGaAs/GaAs quantum dots obtained by the Stranski-Krastanow mode, photons with a near-unity indistinguishability from these quantum emitters have proven to be elusive so far. Here, we show on-demand generation of near-unity indistinguishable photons from these quantum emitters by exploring pulsed resonance fluorescence. Given the short intrinsic lifetime of excitons and trions confined in the GaAs quantum dots, we show single photon indistinguishability with a raw visibility of V-raw = (95.0(-6.1)(+5.0))%, without the need for Purcell enhancement. Our results represent a milestone in the advance of GaAs quantum dots by demonstrating the final missing property standing in the way of using these emitters as a key component in quantum communication applications, e.g., as quantum light sources for quantum repeater architectures.

##### The BCS critical temperature in a weak magnetic field

R. Frank, C. Hainzl, E. Langmann

Journal of Spectral Theory 9 (3), 1005–1062 (2019).

We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order terms. This provides a rigorous derivation and generalization of results obtained in the physics literature fromWHH theory of the upper critical magnetic field. A new ingredient in our proof is a rigorous phase approximation to control the effects of the magnetic field.

##### Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function

A. Dietlein, M. Gebert, P. Müller

J. Spectr. Theory 9, 921 – 965 (2019).

We study effects of a bounded and compactly supported perturbation on multidimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015), 560–565]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b. Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a∈Rd, and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H.

##### Time-dependent study of disordered models with infinite projected entangled pair states

C. Hubig, I. Cirac.

SciPost Physics 6, 031 (2019).

Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or variational optimisation. Here, we show (i) the feasibility of real-time evolution in iPEPS to simulate the dynamics of an infinite system after a global quench and (ii) the application of disorder-averaging to obtain translationally invariant systems in the presence of disorder. To illustrate the approach, we study the short-time dynamics of the square lattice Heisenberg model in the presence of a bi-valued disorder field.

##### Learning multiple order parameters with interpretable machines

K. Liu, J. Greitemann, L. Pollet.

Physical Review B 99, 104410 (2019).

Machine-learning techniques are evolving into a subsidiary tool for studying phase transitions in many-body systems. However, most studies are tied to situations involving only one phase transition and one order parameter. Systems that accommodate multiple phases of coexisting and competing orders, which are common in condensed matter physics, remain largely unexplored from a machine-learning perspective. In this paper, we investigate multiclassification of phases using support vector machines (SVMs) and apply a recently introduced kernel method for detecting hidden spin and orbital orders to learn multiple phases and their analytical order parameters. Our focus is on multipolar orders and their tensorial order parameters whose identification is difficult with traditional methods. The importance of interpretability is emphasized for physical applications of multiclassification. Furthermore, we discuss an intrinsic parameter of SVM, the bias, which allows for a special interpretation in the classification of phases, and its utility in diagnosing the existence of phase transitions. We show that it can be exploited as an efficient way to explore the topology of unknown phase diagrams where the supervision is entirely delegated to the machine.

##### Experimentally reducing the quantum measurement back action in work distributions by a collective measurement

K.D. Wu, Y. Yuan, G.-Y. Xiang, C.-F. Li, G.-C. Guo, M. Perarnau-Llobet

Science Advances 5 (3), eaav4944 (2019).

In quantum thermodynamics, the standard approach to estimating work fluctuations in unitary processes is based on two projective measurements, one performed at the beginning of the process and one at the end. The first measurement destroys any initial coherence in the energy basis, thus preventing later interference effects. To decrease this back action, a scheme based on collective measurements has been proposed by Perarnau-Llobet et al. Here, we report its experimental implementation in an optical system. The experiment consists of a deterministic collective measurement on two identically prepared qubit states, encoded in the polarization and path degree of a single photon. The standard two-projective measurement approach is also experimentally realized for comparison. Our results show the potential of collective schemes to decrease the back action of projective measurements, and capture subtle effects arising from quantum coherence.

##### Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks

H. Boche, G. Janssen, S. Saeedinaeeni.

Journal of Mathematical Physics 60, 022204 (2019).

We derive universal codes for simultaneous transmission of classical messages and entanglement through quantum channels, possibly under the attack of a malignant third party. These codes are robust to different kinds of channel uncertainties. To construct such universal codes, we invoke and generalize the properties of random codes for classical and quantum message transmission through quantum channels. We show these codes to be optimal by giving a multi-letter characterization of regions corresponding to capacity of compound quantum channels for simultaneously transmitting and generating entanglement with classical messages. In addition, we give dichotomy statements in which we characterize the capacity of arbitrarily varying quantum channels for simultaneous transmission of classical messages and entanglement. These include cases where the malignant jammer present in the arbitrarily varying channel model is classical (chooses channel states of the product form) and fully quantum (is capable of general attacks not necessarily of the product form).

##### Density-matrix embedding theory study of the one-dimensional Hubbard-Holstein model

T.E. Reinhard, U. Mordovina, C. Hubig, J.S. Kretchmer, U. Schollwöck, H. Appel, M.A. Sentef, A. Rubio,

Journal of Chemical Theory and Computation 15 (4), 2221-2232 (2019).

We present a density-matrix embedding theory (DMET) study of the one-dimensional Hubbard–Holstein model, which is paradigmatic for the interplay of electron–electron and electron–phonon interactions. Analyzing the single-particle excitation gap, we find a direct Peierls insulator to Mott insulator phase transition in the adiabatic regime of slow phonons in contrast to a rather large intervening metallic phase in the anti-adiabatic regime of fast phonons. We benchmark the DMET results for both on-site energies and excitation gaps against density-matrix renormalization group (DMRG) results and find good agreement of the resulting phase boundaries. We also compare the full quantum treatment of phonons against the standard Born–Oppenheimer (BO) approximation. The BO approximation gives qualitatively similar results to DMET in the adiabatic regime but fails entirely in the anti-adiabatic regime, where BO predicts a sharp direct transition from Mott to Peierls insulator, whereas DMET correctly shows a large intervening metallic phase. This highlights the importance of quantum fluctuations in the phononic degrees of freedom for metallicity in the one-dimensional Hubbard–Holstein model.

##### Interaction quench and thermalization in a one-dimensional topological Kondo insulator

I. Hagymási, C. Hubig, U. Schollwöck

Physical Review B 99, 075145 (2019).

We study the nonequilibrium dynamics of a one-dimensional topological Kondo insulator, modelled by a p-wave Anderson lattice model, following a quantum quench of the on-site interaction strength. Our goal is to examine how the quench influences the topological properties of the system, and therefore our main focus is the time evolution of the string order parameter, entanglement spectrum, and the topologically protected edge states. We point out that postquench local observables can be well captured by a thermal ensemble up to a certain interaction strength. Our results demonstrate that the topological properties after the interaction quench are preserved. Though the absolute value of the string order parameter decays in time, the analysis of the entanglement spectrum, Loschmidt echo and the edge states indicates the robustness of the topological properties in the time-evolved state. These predictions could be directly tested in state-of-the-art cold-atom experiments.

##### Tuning the Frohlich exciton-phonon scattering in monolayer MoS2

B. Miller, J. Lindlau, M. Bommert, A. Neumann, H. Yamaguchi, A. Holleitner, A. Hoegele, U. Wurstbauer

Nature Communications 10, 807 (2019).

Charge carriers in semiconducting transition metal dichalcogenides possess a valley degree of freedom that allows for optoelectronic applications based on the momentum of excitons. At elevated temperatures, scattering by phonons limits valley polarization, making a detailed knowledge about strength and nature of the interaction of excitons with phonons essential. In this work, we directly access exciton-phonon coupling in charge tunable single layer MoS2 devices by polarization resolved Raman spectroscopy. We observe a strong defect mediated coupling between the long-range oscillating electric field induced by the longitudinal optical phonon in the dipolar medium and the exciton. This so-called Frohlich exciton phonon interaction is suppressed by doping. The suppression correlates with a distinct increase of the degree of valley polarization up to 20% even at elevated temperatures of 220 K. Our result demonstrates a promising strategy to increase the degree of valley polarization towards room temperature valleytronic applications.

##### Probing hidden spin order with interpretable machine learning

J. Greitemann, K. Liu, L. Pollet.

Physical Review B 99, 060404(R) (2019).

The search of unconventional magnetic and nonmagnetic states is a major topic in the study of frustrated magnetism. Canonical examples of those states include various spin liquids and spin nematics. However, discerning their existence and the correct characterization is usually challenging. Here we introduce a machine-learning protocol that can identify general nematic order and their order parameter from seemingly featureless spin configurations, thus providing comprehensive insight on the presence or absence of hidden orders. We demonstrate the capabilities of our method by extracting the analytical form of nematic order parameter tensors up to rank 6. This may prove useful in the search for novel spin states and for ruling out spurious spin liquid candidates.

##### Toward femtosecond electronics up to 10 THz

N. Fernandez, P. Zimmermann, P. Zechmann, M. Worle, R. Kienberger, A.W. Holleitner

Ultrafast Phenomena and Nanophotonics XXIII 10916, 109160R (2019).

We numerically compute the effective diffraction index and attenuation of coplanar stripline circuits with microscale lateral dimensions on various substrates including sapphire, GaN, silica glass, and diamond grown by chemical vapor deposition. We show how to include dielectric, radiative and ohmic losses to describe the pulse propagation in the striplines to allow femtosecond on-chip electronics with frequency components up to 10 THz.

##### Non-Ergodic Delocalization in the Rosenzweig-Porter Model

P. von Soosten, Simone Warzel

Letters in Mathematical Physics 109, 905-922 (2019).

We consider the Rosenzweig–Porter model H=V+T????, where V is a N×N diagonal matrix, ? is drawn from the N×N Gaussian Orthogonal Ensemble, and N?1?T?1. We prove that the eigenfunctions of H are typically supported in a set of approximately NT sites, thereby confirming the existence of a previously conjectured non-ergodic delocalized phase. Our proof is based on martingale estimates along the characteristic curves of the stochastic advection equation satisfied by the local resolvent of the Brownian motion representation of H.