##### Magnetism in the two-dimensional dipolar XY model

B. Sbierski, M. Bintz, S. Chatterjee, M. Schuler, N. Y. Yao, L. Pollet

Physical Review B 109 (14), 144411 (2024).

Motivated by a recent experiment on a square-lattice Rydberg atom array realizing a long-range dipolar properties. We obtain the phase diagram, critical properties, entropies, variance of the magnetization, and site-resolved correlation functions. We consider both ferromagnetic and antiferromagnetic interactions and apply quantum Monte Carlo and pseudo-Majorana functional renormalization group techniques, generalizing the latter to a U (1) symmetric setting. Our simulations perform extensive thermometry in dipolar Rydberg atom arrays and establish conditions for adiabaticity and thermodynamic equilibrium. On the ferromagnetic side of the experiment, we determine the entropy per particle S/N approximate to 0.5, close to the one at the critical temperature, Sc/N = 0.585(15). The simulations suggest the presence of an out-of-equilibrium plateau at large distances in the correlation function, thus motivating future studies on the nonequilibrium dynamics of the system.

##### Exotic symmetry breaking properties of self-dual fracton spin models

G. Canossa, L. Pollet, M. A. Martin-Delgado, H. Song, K. Liu

Physical Review Research 6 (1), 13304 (2024).

Fracton codes host unconventional topological states of matter and are promising for fault -tolerant quantum computation due to their large coding space and strong resilience against decoherence and noise. In this paper, we investigate the ground -state properties and phase transitions of two prototypical self -dual fracton spin models-the tetrahedral Ising model and the fractal Ising model-which correspond to error -correction procedures for the representative fracton codes of type I and type II, the checkerboard code and the Haah's code, respectively, in the error -free limit. They are endowed with exotic symmetry -breaking properties that contrast sharply with the spontaneous breaking of global symmetries and deconfinement transition of gauge theories. To show these unconventional behaviors, which are associated with subdimensional symmetries, we construct and analyze the order parameters, correlators, and symmetry generators for both models. Notably, the tetrahedral Ising model acquires an extended semilocal ordering moment, while the fractal Ising model fits into a polynomial ring representation and leads to a fractal order parameter. Numerical studies combined with analytical tools show that both models experience a strong first -order phase transition with an anomalous L -(D-1) scaling, despite the fractal symmetry of the latter. Our paper provides a unique understanding of subdimensional symmetry breaking and makes an important step for studying quantum -error -correction properties of the checkerboard and Haah's codes.

##### Universal correlations as fingerprints of transverse quantum fluids

A. Kuklov, L. Pollet, N. Prokof'ev, L. Radzihovsky, B. Svistunov

Physical Review A 109 (1), L011302 (2024).

We study universal off -diagonal correlations in transverse quantum fluids (TQF),. a new class of quasi -onedimensional superfluids featuring long -range -ordered ground states. These exhibit unique self -similar space-time relations scaling with x2/D tau that serve as fingerprints of the specific states. The results obtained with the effective field theory are found to be in perfect agreement with ab initio simulations of hard-core bosons on a lattice,. a simple microscopic realization of TQF. This allows an accurate determination-at nonzero temperature and finite system size-of such key ground -state properties as the condensate and superfluid densities, and characteristic parameter D.

##### The classical Heisenberg model on the centred pyrochlore lattice

R. P. Nutakki, L. D. C. Jaubert, L. Pollet

Scipost Physics 15 (2), 40 (2023).

The centred pyrochlore lattice is a novel geometrically frustrated lattice, realized in the metal-organic framework Mn(ta)2 [1] where the basic unit of spins is a five site centred tetrahedron. Here, we present an in-depth theoretical study of the J1 - J2 classical Heisenberg model on this lattice, using a combination of mean-field analytical methods and Monte Carlo simulations. We find a rich phase diagram with low temperature states exhibiting ferrimagnetic order, partial ordering, and a highly degenerate spin liquid with distinct regimes of low temperature correlations. We discuss in detail how the regime displaying broadened pinch points in its spin structure factor is consistent with an effective description in terms of a fluid of interacting charges. We also show how this picture holds in two dimensions on the analogous centred kagome lattice and elucidate the connection to the physics of thin films in (d + 1) dimensions. Furthermore, we show that a Coulomb phase can be stabilized on the centred pyrochlore lattice by the addition of further neighbour couplings. This demonstrates the centred pyrochlore lattice is an experimentally relevant geometry which naturally hosts emergent gauge fields in the presence of charges at low energies.

##### Frustration on a centered pyrochlore lattice in metal-organic frameworks

R. P. Nutakki, R. Röss-Ohlenroth, D. Volkmer, A. Jesche, H. A. K. von Nidda, A. A. Tsirlin, P. Gegenwart, L. Pollet, L. D. C. Jaubert

Physical Review Research 5 (2), L022018 (2023).

Geometric frustration inhibits magnetic systems from ordering, opening a window to unconventional phases of matter. The paradigmatic frustrated lattice in three dimensions to host a spin liquid is the pyrochlore, although there remain few experimental compounds thought to realize such a state. Here, we go beyond the pyrochlore via molecular design in the metal-azolate framework [Mn(II)(ta)2], which realizes a closely related centered pyrochlore lattice of Mn spins with S = 5/2. Despite a Curie-Weiss temperature of -21 K indicating the energy scale of magnetic interactions, [Mn(II)(ta)2] orders at only 430 mK, putting it firmly in the category of highly frustrated magnets. Comparing magnetization and specific-heat measurements to numerical results for a minimal Heisenberg model, we predict that this material displays distinct features of a classical spin liquid with a structure factor reflecting Coulomb physics in the presence of charges.

##### Robust stripes in the mixed-dimensional t-J model

H. Schlömer, A. Bohrdt, L. Pollet, U. Schollwöck, F. Grusdt

Physical Review Research 5 (2), L022027 (2023).

Microscopically understanding competing orders in strongly correlated systems is a key challenge in modern quantum many-body physics. For example, the origin of stripe order and its relation to pairing in the Fermi -Hubbard model remains one of the central questions, and may help to understand the origin of high-temperature superconductivity in cuprates. Here, we analyze stripe formation in the doped mixed-dimensional (mixD) variant of the t - J model, where charge carriers are restricted to move only in one direction, whereas magnetic SU(2) interactions are two-dimensional. Using the density matrix renormalization group at finite temperature, we find a stable vertical stripe phase in the absence of pairing, featuring incommensurate magnetic order and long-range charge density wave profiles over a wide range of dopings. We find high critical temperatures on the order of the magnetic coupling similar to J/2, hence being within reach of current quantum simulators. Snapshots of the many-body state, accessible to quantum simulators, reveal hidden spin correlations in the mixD setting, whereby antiferromagnetic correlations are enhanced when considering purely the magnetic background. The proposed model can be viewed as realizing a parent Hamiltonian of the stripe phase, whose hidden spin correlations lead to the predicted resilience against quantum and thermal fluctuations.

##### Hybrid symmetry breaking in classical spin models with subsystem symmetries

G. Canossa, L. Pollet, K. Liu

Physical Review B 107 (5), 54431 (2023).

We investigate two concrete cases of phase transitions breaking a subsystem symmetry. The models are two classical compass models featuring line-flip and plane-flip symmetries and correspond to special limits of a Heisenberg-Kitaev Hamiltonian on a cubic lattice. We show that these models experience a hybrid symmetry breaking by which the system display distinct symmetry broken patterns in different submanifolds. For instance, the system may look magnetic within a chain or plane but nematic-like when observing from one dimensionality higher. We fully characterize the symmetry-broken phases by a set of subdimensional order parameters and confirm numerically both cases undergo a non-standard first-order phase transition. Our results provide new insights into phase transitions involving subsystem symmetries and generalize the notion of conventional spontaneous symmetry breaking.

##### Competing instabilities at long length scales in the one-dimensional Bose-Fermi-Hubbard model at commensurate fillings

J. Schönmeier-Kromer, L. Pollet

Physical Review B 107 (5), 54502 (2023).

We study the phase diagram of the one-dimensional Bose-Fermi-Hubbard model at unit filling for the scalar bosons and half filling for the S = 1/2 fermions using quantum Monte Carlo simulations. The bare interaction between the fermions is set to zero. A central question of our study is what type of interactions can be induced between the fermions by the bosons, for both weak and strong interspecies coupling. We find that the induced interactions can lead to competing instabilities favoring phase separation, superconducting phases, and density wave structures, in many cases at work on length scales of more than 100 sites. Marginal bosonic superfluids with a density matrix decaying faster than what is allowed for pure bosonic systems with on-site interactions, are also found.

##### Phase diagram of mixed-dimensional anisotropic t-J models

J. Dicke, L. Rammelmüller, F. Grusdt, L. Pollet

Physical Review B 107 (7), 75109 (2023).

We study the phase diagram of two different mixed-dimensional t-Jz-J1 models on the square lattice, in which the hopping amplitude t is only nonzero along the x direction. In the first model, which is bosonic, the spin-exchange amplitude J1 is negative and isotropic along the x and y directions of the lattice, and Jz is isotropic and positive. The low-energy physics is characterized by spin-charge separation: the holes hop as free fermions in an easy-plane ferromagnetic background. In the second model, J1 is restricted to the x axis while Jz remains isotropic and positive. The model is agnostic to particle statistics, and shows stripe patterns with antiferromagnetic Neel order at low temperature and high hole densities, in resemblance of the mixed-dimensional t-Jz and t -J models. At lower hole density, a very strong first-order transition and hysteresis loop is seen extending to a remarkably high 14(1)% hole doping.

##### Unsupervised interpretable learning of phases from many-qubit systems

N. Sadoune, G. Giudici, K. Liu, L. Pollet

Physical Review Research 5 (1), 13082 (2023).

Experimental progress in qubit manufacturing calls for the development of new theoretical tools to analyze quantum data. We show how an unsupervised machine-learning technique can be used to understand short -range entangled many-qubit systems using data of local measurements. The method successfully constructs the phase diagram of a cluster-state model and detects the respective order parameters of its phases, including string order parameters. For the toric code subject to external magnetic fields, the machine identifies the explicit forms of its two stabilizers. Prior information of the underlying Hamiltonian or the quantum states is not needed,. instead, the machine outputs their characteristic observables. Our work opens the door for a first-principles application of hybrid algorithms that aim at strong interpretability without supervision.

##### Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry

H. Song, J. Schönmeier-Kromer, K. Liu, O. Viyuela, L. Pollet, M. A. Martin-Delgado

Physical Review Letters 129 (23), 230502 (2022).

Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for quantum error correcting codes based on fracton models. By mapping the error-correction process for bit-flip and phase-flip noises into novel statistical models with Ising variables and random multibody couplings, we obtain models that exhibit an unconventional subsystem symmetry instead of a more usual global symmetry. We perform large-scale parallel tempering Monte Carlo simulations to obtain disorder-temperature phase diagrams, which are then used to predict optimal error thresholds for the corresponding fracton code. Remarkably, we found that the X-cube fracton code displays a minimum error threshold (7.5%) that is much higher than 3D topological codes such as the toric code (3.3%), or the color code (1.9%). This result, together with the predicted absence of glass order at the Nishimori line, shows great potential for fracton phases to be used as quantum memory platforms.

##### Supertransport by Superclimbing Dislocations in He-4: When All Dimensions Matter

A. B. Kuklov, L. Pollet, N. V. Prokof'ev, B. V. Svistunov

Physical Review Letters 128 (25), 255301 (2022).

The unique superflow-through-solid effect observed in solid 4He and attributed to the quasi-onedimensional superfluidity along the dislocation cores exhibits two extraordinary features: (i) an exponentially strong suppression of the flow by a moderate increase in pressure and (ii) an unusual temperature dependence of the flow rate with no analogy to any known system and in contradiction with the standard Luttinger liquid paradigm. Based on ab initio and model simulations, we argue that the two features are closely related: Thermal fluctuations of the shape of a superclimbing edge dislocation induce large, correlated, and asymmetric stress fields acting on the superfluid core. The critical flux is most sensitive to strong rare fluctuations and hereby acquires a sharp temperature dependence observed in experiments.

##### Light-Induced Quantum Droplet Phases of Lattice Bosons in Multimode Cavities

P. Karpov, F. Piazza

Physical Review Letters 128 (10), 103201 (2022).

Multimode optical cavities can be used to implement interatomic interactions which are highly tunable in strength and range. For bosonic atoms trapped in an optical lattice we show that, for any finite range of the cavity-mediated interaction, quantum self-bound droplets dominate the ground state phase diagram. Their size and in turn density is not externally fixed but rather emerges from the competition between local repulsion and finite-range cavity-mediated attraction. We identify two different regimes of the phase diagram. In the strongly glued regime, the interaction range exceeds the droplet size and the physics resembles the one of the standard Bose-Hubbard model in a (self-consistent) external potential, where in the phase diagram two incompressible droplet phases with different filling are separated by one with a superfluid core. In the opposite weakly glued regime, we find instead direct first order transitions between the two incompressible phases, as well as pronounced metastability. The cavity field leaking out of the mirrors can be measured to distinguish between the various types of droplets.

##### Machine-learned phase diagrams of generalized Kitaev honeycomb magnets

N. Rao, K. Liu, M. Machaczek, L. Pollet

Physical Review Research 3 (3), 33223 (2021).

We use a recently developed interpretable and unsupervised machine-learning method, the tensorial kernel support vector machine, to investigate the low-temperature classical phase diagram of a generalized HeisenbergKitaev-Gamma (J-K-F) model on a honeycomb lattice. Aside from reproducing phases reported by previous quantum and classical studies, our machine finds a hitherto missed nested zigzag-stripy order and establishes the robustness of a recently identified modulated S-3 x Z(3) phase, which emerges through the competition between the Kitaev and Gamma spin liquids, against Heisenberg interactions. The results imply that, in the restricted parameter space spanned by the three primary exchange interactions-J, K, and Gamma, the representative Kitaev material alpha-RuCl3 lies close to the boundaries of several phases, including a simple ferromagnet, the unconventional S-3 x Z(3), and nested zigzag-stripy magnets. A zigzag order is stabilized by a finite Gamma' and/or J(3) term, whereas the four magnetic orders may compete in particular if Gamma' is antiferromagnetic.

##### Inferring hidden symmetries of exotic magnets from detecting explicit order parameters

N. Rao, K. Liu, L. Pollet

Physical Review E 104 (1), 15311 (2021).

An unconventional magnet may be mapped onto a simple ferromagnet by the existence of a high-symmetry point. Knowledge of conventional ferromagnetic systems may then be carried over to provide insight into more complex orders. Here we demonstrate how an unsupervised and interpretable machine-learning approach can be used to search for potential high-symmetry points in unconventional magnets without any prior knowledge of the system. The method is applied to the classical Heisenberg-Kitaev model on a honeycomb lattice, where our machine learns the transformations that manifest its hidden O(3) symmetry, without using data of these high-symmetry points. Moreover, we clarify that, in contrast to the stripy and zigzag orders, a set of D2 and D2h ordering matrices provides a more complete description of the magnetization in the Heisenberg-Kitaev model. In addition, our machine also learns the local constraints at the phase boundaries, which manifest a subdimensional symmetry. This paper highlights the importance of explicit order parameters to many-body spin systems and the property of interpretability for the physical application of machine-learning techniques.

##### Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase

L. Rammelmuller, Y. Q. Hou, J. E. Drut, J. Braun

Physical Review A 103 (4), 43330 (2021).

We theoretically study the pairing behavior of the unitary Fermi gas in the normal phase. Our analysis is based on the static spin susceptibility, which characterizes the response to an external magnetic field. We obtain this quantity by means of the complex Langevin approach and compare our calculations to available literature data in the spin-balanced case. Furthermore, we present results for polarized systems, where we complement and expand our analysis at high temperature with high-order virial expansion results. The implications of our findings for the phase diagram of the spin-polarized unitary Fermi gas are discussed in the context of the state of the art.

##### Revealing the phase diagram of Kitaev materials by machine learning: Cooperation and competition between spin liquids

K. Liu, N. Sadoune, N. Rao, J. Greitemann, L. Pollet

Physical Review Research 3 (2), 23016 (2021).

Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-Gamma model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic S3 magnets, and two modulated S-3 x Z(3) magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-S limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two S-3 x Z(3) orders are induced by competition between Kitaev and Gamma spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.

##### The view of TK-SVM on the phase hierarchy in the classical kagome Heisenberg antiferromagnet

J. Greitemann, K. Liu, L. Pollet

Journal of Physics-Condensed Matter 33 (5), 54002 (2021).

We illustrate how the tensorial kernel support vector machine (TK-SVM) can probe the hidden multipolar orders and emergent local constraint in the classical kagome Heisenberg antiferromagnet. We show that TK-SVM learns the finite-temperature phase diagram in an unsupervised way. Moreover, in virtue of its strong interpretability, it identifies the tensorial quadrupolar and octupolar orders, which define a biaxial D-3h spin nematic, and the local constraint that underlies the selection of coplanar states. We then discuss the disorder hierarchy of the phases, which can be inferred from both the analytical order parameters and an SVM bias parameter. For completeness we mention that the machine also picks up the leading 3x3<i correlations in the dipolar channel at very low temperature, which are however weak compared to the quadrupolar and octupolar orders. Our work shows how TK-SVM can facilitate and speed up the analysis of classical frustrated magnets.

##### Z(2) Parton Phases in the Mixed-Dimensional t - J(z) Model

F. Grusdt, L. Pollet

Physical Review Letters 125 (25), 256401 (2020).

We study the interplay of spin and charge degrees of freedom in a doped Ising antiferromagnet, where the motion of charges is restricted to one dimension. The phase diagram of this mixed-dimensional t - J(z) model can be understood in terms of spinless chargons coupled to a Z(2) lattice gauge field. The antiferromagnetic couplings give rise to interactions between Z(2) electric field lines which, in turn, lead to a robust stripe phase at low temperatures. At higher temperatures, a confined meson-gas phase is found for low doping whereas at higher doping values, a robust deconfined chargon-gas phase is seen, which features hidden antiferromagnetic order. We confirm these phases in quantum Monte Carlo simulations. Our model can be implemented and its phases detected with existing technology in ultracold atom experiments. The critical temperature for stripe formation with a sufficiently high hole concentration is around the spin-exchange energy J(z), i.e., well within reach of current experiments.

##### Constrained random phase approximation of the effective Coulomb interaction in lattice models of twisted bilayer graphene

T. I. Vanhala, L. Pollet

Physical Review B 102 (3), 35154 (2020).

Recent experiments on twisted bilayer graphene show the urgent need for establishing a low-energy lattice model for the system. We use the constrained random phase approximation to study the interaction parameters of such models, taking into account screening from the moire bands left outside the model space. Based on an atomic-scale tight-binding model, we numerically compute the polarization function and study its behavior for different twist angles. We discuss an approximation scheme which allows us to compute the screened interaction, in spite of the very large number of atoms in the unit cell. We find that the polarization has three different momentum regimes. For small momenta, the polarization is quadratic, leading to a linear dielectric function expected for a two-dimensional dielectric material. For large momenta, the polarization becomes independent of the twist angle and approaches that of uncoupled graphene layers. In the intermediate-momentum regime, the dependence on the twist angle is strong. Close to the largest magic angle the dielectric function peaks at a momentum of 1/(4 nm), attaining values of 18-25, depending on the exact model, meaning very strong screening at intermediate distances. We also calculate the effective screened Coulomb interaction in real space and give estimates for the on-site and extended interaction terms for the recently developed hexagonal-lattice model. For freestanding twisted bilayer graphene, the effective interaction decays slower than 1/r at intermediate distances r, while it remains essentially unscreened at large enough r.

##### 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.

##### 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.

##### Polaron Mobility in the ""Beyond Quasiparticles"" Regime

A. S. Mishchenko, L. Pollet, N. V. Prokof'ev, A. Kumar, D. L. Maslov, N. Nagaosa

Physical Review Letters 123 (7), 76601 (2019).

"In a number of physical situations, frompolarons to Dirac liquids and to non-Fermi liquids, one encounters the ""beyond quasiparticles"" regime, in which the inelastic scattering rate exceeds the thermal energy of quasiparticles. Transport in this regime cannot be described by the kinetic equation. We employ the diagrammatic Monte Carlo method to study the mobility of a Frohlich polaron in this regime and discover a number of nonperturbative effects: a strong violation of the Mott-Ioffe-Regel criterion at intermediate and strong couplings, a mobility minimum at T similar to Omega in the strong-coupling limit (Omega is the optical mode frequency), a substantial delay in the onset of an exponential dependence of the mobility for T < Omega at intermediate coupling, and complete smearing of the Drude peak at strong coupling. These effects should be taken into account when interpreting mobility data in materials with strong electron-phonon coupling."

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

K. Liu, J. Greitemann, L. Pollet

Physical Review B 99 (10), 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.

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

J. Greitemann, K. Liu, L. Pollet

Physical Review B 99 (6), 60404 (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.