Understanding which minimal effective model captures the essential physics of cuprates is a key step towards unraveling the mechanism behind high-Tc superconductivity. Recent measurements of the dynamical spin structure factor (DSF) in cuprate ladder compounds have indicated the presence of an additional, attractive term in the single-band Hubbard model, potentially originating from electron-phonon interactions. Here, we demonstrate that similar DSF features can also be captured by t-J descriptions with a smaller attractive term. Motivated by this observation, we systematically investigate the strength and origin of different contributions to the single-band Hamiltonians by downfolding either from the three-band Emery model or the electron-phonon coupled Hubbard-Holstein model. For one-dimensional systems, we find that the extended versions of both single-band descriptions can reproduce the experimentally observed DSF signatures. Finally, we extend our analysis to two dimensions by comparing two-hole correlation functions for the different single-band models. Our results provide new insights into the long-standing question of which single-band Hamiltonian can capture the essential physics of cuprates.

"In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual ""pseudogap"" metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of dopings and temperatures in a regime where a pseudogap is known to develop. By measuring multipoint correlation functions up to fifth order, we uncover a universal scaling behavior in magnetic and higher-order spin-charge correlations characterized by a doping-dependent temperature scale. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this temperature scale is comparable to the pseudogap temperature T & lowast,.. Our quantitative findings reveal a qualitative behavior of magnetic properties and spin-charge correlations in an emergent pseudogap and pave the way toward the exploration of charge pairing and collective phenomena expected at lower temperatures."

Simulating the dynamics of many-body quantum systems is a significant challenge, especially in higher dimensions where entanglement grows rapidly. Neural quantum states (NQS) offer a promising tool for representing quantum wavefunctions, but their application to time evolution faces scaling challenges. We introduce the time-dependent neural quantum state (t-NQS), a novel approach incorporating explicit time dependence into the neural network ansatz. This framework optimizes a single, time-independent set of parameters to solve the time-dependent Schr & ouml,.dinger equation across an entire time interval. We detail an autoregressive, attention-based transformer architecture and techniques for extending the model's applicability. To benchmark and demonstrate our method, we simulate quench dynamics in the 2D transverse field Ising model and the time-dependent preparation of the 2D antiferromagnetic state in a Heisenberg model, demonstrating state of the art performance, scalability, and extrapolation to unseen intervals. These results establish t-NQS as a powerful framework for exploring quantum dynamics in strongly correlated systems.

"The competition of different length scales in quantum many-body systems leads to phenomena such as correlated dynamics and nonlocal order. To investigate such effects in an itinerant lattice-based quantum simulator, it has been proposed to introduce tunable extended-range interactions using off-resonant optical coupling to Rydberg states, known as Rydberg dressing. In this work, we use this approach to realize an effective one-dimensional extended Bose-Hubbard model. Harnessing our quantum gas microscope, we probe the correlated out-of-equilibrium dynamics of extended-range repulsively bound pairs and ""hard rods."" By contrast, operating near equilibrium, we observe density ordering when adiabatically turning on the extended-range interactions. Our results pave the way to realizing light-controlled extended-range interacting quantum many-body systems."

Due to significant progress in quantum gas microscopy in recent years, there is a rapidly growing interest in real-space properties of single mobile dopands created in correlated antiferromagnetic (AFM) Mott insulators. However, a detailed numerical description remains challenging, even for simple toy models. As a consequence, previous numerical simulations for large systems were largely limited to T = 0. To provide guidance for cold-atom experiments, numerical calculations at finite temperature are required. Here, we numerically study the real-time properties of a single mobile hole in the 2D t-J model at finite temperature and draw a comparison to features observed at T = 0. We find that a three-stage process of hole motion, which was reported at T = 0, is valid even at finite temperature. However, already at low temperatures, the average hole velocity at long times is not simply proportional to the spin coupling, contrary to the T = 0 behavior. Comparing our finite-temperature numerical results with the experimental data from quantum gas microscopy we find a qualitative disagreement: in experiment, hole spreading speeds up with increasing J/t, while in our numerics it slows down. The latter is consistent with the numerical findings previously reported at T = 0.

The physics of strongly correlated fermions described by Hubbard or t-J models in the underdoped regime- relevant for high-temperature superconductivity in cuprate compounds-remains a subject of ongoing debate. In particular, the nature of charge carriers in this regime is poorly understood, in part due to the unusual properties of their spectral function. In this Letter, we present unbiased numerical results for the one-hole spectral function in a t-J model at finite temperatures. Our study provides valuable insights into the underlying physics of magnetic (or spin-) polaron formation in a doped antiferromagnet (AFM). For example, we find how the suppression of spectral weight outside the magnetic Brillouin zone-a precursor of Fermi arc formation-disappears with increasing temperature, revealing nearly-deconfined spinon excitations of the undoped AFM. The pristine setting we consider can be directly explored using quantum simulators. Our calculations demonstrate that coherent quasiparticle peaks associated with magnetic polarons can be observed up to temperatures T > J above the spin-exchange J, routinely obtained in such experiments. This paves the way for future studies of the fate of magnetic polarons in the pseudogap phase.

Simulating large, strongly interacting fermionic systems remains a major challenge for existing numerical methods. In this Letter, we introduce Gutzwiller projected hidden fermion determinant states (G-HFDS) to simulate the strongly interacting limit of the Fermi-Hubbard model, namely the t-J model, across the entire doping regime. We demonstrate that the G-HFDS achieve energies competitive with matrix product states on lattices as large as 10 x 10 sites while using several orders of magnitude fewer parameters, suggesting the potential for efficient application to even larger system sizes. This remarkable efficiency enables us to probe low-energy physics across the full doping range, providing new insights into the competition between kinetic and magnetic interactions and the nature of emergent quasiparticles. Starting from the low-doping regime, where magnetic polarons dominate the low energy physics, we track their evolution with increasing doping and different next-nearest neighbor hopping amplitudes through analyses of spin and polaron correlation functions as well as the Fermi surface. Our findings demonstrate the potential of determinant-based neural quantum states with an inherent fermionic sign structure, opening the way for simulating large-scale fermionic systems at any particle filling.

Understanding the physics of the two-dimensional Hubbard model is widely believed to be a key step in achieving a full understanding of high-Tc cuprate superconductors. In recent years, progress has been made by large-scale numerical simulations at finite doping and, on the other hand, by microscopic theories able to capture the physics of individual charge carriers. In this work, we study single pairs of dopants in a cylindrical system using the density-matrix renormalization group algorithm. We identify two coexisting charge configurations that couple to the spin environment in different ways: a tightly bound configuration featuring (next-)nearest-neighbor pairs and a stripelike configuration of dopants on opposite sides of the cylinder, accompanied by a spin domain wall. Thus, we establish that the interplay between stripe order and uniform pairing, central to the models' phases at finite doping, has its origin at the single-pair level. By interpolating between the Hubbard and the related t-J model, we are able to quantitatively understand discrepancies in the pairing properties of the two models through the three-site hopping term usually omitted from the t-J Hamiltonian. This term is closely related to a next-nearest-neighbor tunneling t', which we observe to upset the balance between the competing stripe and pair states on the two-dopant level.

One of the key features of hole-doped cuprates is the presence of an extended pseudogap phase, whose microscopic origin has been the subject of intense investigation since its discovery and is believed to be crucial for understanding high-temperature superconductivity. Various explanations have been proposed for the pseudogap, including links to symmetry-breaking orders such as stripes or pairing, and the emergence of novel fractionalized Fermi liquid (FL & lowast,.) and orthogonal metal (OM) phases. The topological nature of FL & lowast,. and OM phases has been identified as scenarios compatible with a small Fermi surface without symmetry breaking, as suggested experimentally. With recent experimental and numerical studies supporting an intricate relationship between stripe order and the pseudogap phase, we here propose an alternative scenario: an orthogonal metal with a geometric origin (GOM) driven by fluctuating domain walls. The essential mechanism behind our proposal is hidden order, where the proliferation of domain walls stabilized by charge fluctuations obscures the underlying long-range antiferromagnetic order in real space, but order is preserved in the reference frame of the background spins. As a result, well-defined fermionic quasiparticles in the form of magnetic polarons exist, which couple to Z2 topological excitations of the domain-wall string-net condensate in the ground state and constitute a small Fermi surface. At a critical doping value, we argue that hidden order is lost, driving a transition to a regular Fermi liquid at a hidden quantum critical point featuring quantum critical transport properties. Our GOM framework establishes a deep connection between the antiferromagnetic, stripe, and pseudogap phases, and suggests a possible unification of superconductivity in (electron- and hole-) doped cuprates and heavy fermion compounds.

Doping an antiferromagnetic (AFM) Mott insulator is central to our understanding of a variety of phenomena in strongly correlated electrons, including high-temperature superconductors(1,2). To describe the competition between tunnelling t of hole dopants and AFM spin interactions J, theoretical and numerical studies often focus on the paradigmatic t-J model(3) and the direct analogue quantum simulation of this model in the relevant regime of high-particle density has long been sought(4,5). Here we realize a doped quantum antiferromagnet with next-nearest-neighbour (NNN) tunnellings t (refs.(6, 7, 8, 9-10)) and hard-core bosonic holes(11) using a Rydberg tweezer platform. We use coherent dynamics between three Rydberg levels, encoding spins and holes(12), to implement a tunable bosonic t-J-V model allowing us to study previously inaccessible parameter regimes. We observe dynamical phase separation between hole and spin domains for |t/J|<< 1 and demonstrate the formation of repulsively bound hole pairs in a variety of spin backgrounds. The interference between NNN tunnellings t ' and perturbative pair tunnelling gives rise to light and heavy pairs depending on the sign of t. Using the single-site control allows us to study the dynamics of a single hole in 2D square lattice (anti)ferromagnets. The model we implement extends the toolbox of Rydberg tweezer experiments beyond spin-1/2 models(13) to a larger class of t-J and spin-1 models(14,15).

Due to their inherent capabilities of capturing non-local dependencies, Transformer neural networks have quickly been established as the paradigmatic architecture for large language models and image processing. Next to these traditional applications, machine learning (ML) methods have also been demonstrated to be versatile tools in the analysis of image-like data of quantum phases of matter, e.g. given snapshots of many-body wave functions obtained in ultracold atom experiments. While local correlation structures in image-like data of physical systems can reliably be detected, identifying phases of matter characterized by global, non-local structures with interpretable ML methods remains a challenge. Here, we introduce the correlator Transformer (CoTra), which classifies different phases of matter while at the same time yielding full interpretability in terms of physical correlation functions. The network's underlying structure is a tailored attention mechanism, which learns efficient ways to weigh local and non-local correlations for a successful classification. We demonstrate the versatility of the CoTra by detecting local order in the Heisenberg antiferromagnet, and show that local gauge constraints in one- and two-dimensional lattice gauge theories can be identified. Furthermore, we establish that the CoTra reliably detects non-local structures in images of correlated fermions in momentum space (Cooper pairs) and that it can distinguish percolating from non-percolating images.

Owing to their great expressivity and versatility, neural networks have gained attention for simulating large two-dimensional quantum many-body systems. However, their expressivity comes with the cost of a challenging optimization due to the in general rugged and complicated loss landscape. Here, we present a hybrid optimization scheme for neural quantum states (NQS), involving a data-driven pretraining with numerical or experimental data and a second, Hamiltonian-driven optimization stage. By using both projective measurements from the computational basis as well as expectation values from other measurement configurations such as spin-spin correlations, our pretraining gives access to the sign structure of the state, yielding improved and faster convergence that is robust w.r.t. experimental imperfections and limited datasets. We apply the hybrid scheme to the ground state search for the 2D transverse field Ising model and dipolar XY model on 6 x 6 and 10 x 10 square lattices with a patched transformer wave function, using numerical data as well as experimental data from a programmable Rydb erg quantum simulator [Chen et al., Nature 616 (2023)], and show that the information from a second measurement basis highly improves the performance. Our work paves the way for a reliable and efficient optimization of neural quantum states.

Experimental and numerical spectroscopy have revealed rich physics in antiferromagnets, in particular in frustrated and doped systems. The Majumdar-Ghosh (MG) model has an analytically known spin-disordered ground state of dimerized singlets as a result of magnetic frustration. Here we study the single-hole angleresolved photoemission spectrum (ARPES) of a doped MG model, where we introduce a spin-hole interaction that is experimentally accessible with ultracold molecules. We report abound spinon-holon ground state and clear signatures of a spinon-holon molecule state and polarons in the ARPES spectrum at different magnetizations. Moreover, we find signatures of an emergent Feshbach resonance with tunable interactions associated with the unbinding of the spinon and the holon. Our results provide new insights into the physics of dopants in frustrated t-J models and establish the latter as a new platform for studies of emergent few-body phenomena.

Neural quantum states (NQSs) have emerged as a powerful ansatz for variational quantum Monte Carlo studies of strongly correlated systems. Here, we apply recurrent neural networks (RNNs) and autoregressive transformer neural networks to the Fermi-Hubbard and the (non-Hermitian) Hatano-Nelson-Hubbard models in one and two dimensions. In both cases, we observe that the convergence of the RNN ansatz is challenged when increasing the interaction strength. We present a physically motivated and easy-to-implement strategy for improving the optimization, namely, by ramping of the model parameters. Furthermore, we investigate the advantages and disadvantages of the autoregressive sampling property of both network architectures. For the Hatano-Nelson-Hubbard model, we identify convergence issues that stem from the autoregressive sampling scheme in combination with the non-Hermitian nature of the model. Our findings provide insights into the challenges of the NQS approach and make the first step towards exploring strongly correlated electrons using this ansatz.

The analytical study of confinement in lattice gauge theories (LGTs) remains a difficult task to this day. Taking a geometric perspective on confinement, we develop a real-space renormalization group (RG) formalism for Z(2) LGTs using percolation probability as a confinement order parameter. The RG flow we analyze is constituted by both the percolation probability and the coupling parameters. We consider a classical Z(2) LGT in two dimensions, with matter and thermal fluctuations, and analytically derive the confinement phase diagram. We find good agreement with numerical and exact benchmark results and confirm that a finite matter density enforces confinement at T < infinity in the model we consider. Our RG scheme enables future analytical studies of Z(2) LGTs with matter and quantum fluctuations and beyond.

Due to their immense representative power, neural network quantum states (NQS) have gained significant interest in current research. In recent advances in the field of NQS, it has been demonstrated that this approach can compete with state-of-the-art numerical techniques, making NQS a compelling alternative, in particular for the simulation of large, two-dimensional (2D) quantum systems. In this study, we show that recurrent neural network (RNN) wave functions can be employed to study systems relevant to current research in quantum many- body physics. Specifically, we employ a 2D tensorized gated RNN to explore the bosonic Hofstadter model with a variable local Hilbert space cutoff and long-range interactions. At first, we benchmark the RNN-NQS for the Hofstadter-Bose-Hubbard (HBH) Hamiltonian on a square lattice. We find that this method, despite the complexity of the wave function, is capable of efficiently identifying and representing most ground-state properties. Afterwards, we apply the method to an even more challenging model for current methods, namely, the Hofstadter model with long-range interactions. This model describes Rydberg-dressed atoms on a lattice subject to a synthetic magnetic field. We study systems of size up to 12 x 12 sites and identify three different regimes by tuning the interaction range and the filling fraction nu. In addition to phases known from the HBH model at short-range interaction, we observe bubble crystals and Wigner crystals for long-range interactions. Especially interesting is the evidence of a bubble crystal phase on a lattice, as this gives experiments a starting point for the search of clustered liquid phases, possibly hosting non-Abelian anyon excitations. In our work, we show that NQS are an efficient and reliable simulation method for quantum systems, which are the subject of current research. In particular, we demonstrate the ability of this method to simulate challenging systems with long-range interactions.

Fermi surface reconstruction in cuprates can lead to an abrupt change in the Fermi momentum kF between different phases. This phenomenon remains a subject of debate and is at the heart of an ongoing discussion about the nature of the metallic state in the pseudogap regime. Here we study a minimal model of a kF changing crossover in the one-dimensional Fermi-Hubbard model, where a tuning of the on-site interaction leads to a crossover between a spin-1/2 Luttinger liquid with small Fermi momentum and a spinless chargon liquid with large Fermi momentum. We attribute this to an emergent U (1) symmetry in the strongly correlated limit, which can be used to derive a modified Luttinger sum rule recovering the large Fermi momentum. We analyze Friedel oscillations at the edge of a system to directly probe the change of Fermi momentum at zero and nonzero temperature. This paves the way for a direct experimental observation of changes of the Fermi momentum using ultracold fermions in a quantum gas microscope, with possible extensions to higher dimensional systems.

Resonant interactions associated with the emergence of a bound state constitute one of the cornerstones of modern many-body physics. Here we present a Feshbach perspective on the origin of strong pairing in Fermi-Hubbard type models. We perform a theoretical analysis of interactions between spin-polaron charge carriers in doped Mott insulators, modeled by a near-resonant two-channel scattering problem, and report evidence for Feshbach-type interactions in the dx2-y2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${d}_{{x}<^>{2}-{y}<^>{2}}$$\end{document} channel, consistent with the established phenomenology of cuprates. Existing experimental and numerical results on hole-doped cuprates lead us to conjecture the existence of a light, long-lived, low-energy excited state of two holes, which enables near-resonant interactions. To put our theory to a test we suggest to use coincidence angle-resolved photoemission spectroscopy (cARPES), pair-tunneling measurements or pump-probe experiments. The emergent Feshbach resonance among spin-polarons could also underlie superconductivity in other doped antiferromagnetic Mott insulators highlighting its potential as a unifying strong-coupling pairing mechanism rooted in quantum magnetism.

The relation between d-wave superconductivity and stripes is fundamental to the understanding of ordered phases in high-temperature cuprate superconductors1, 2, 3, 4, 5-6. These phases can be strongly influenced by anisotropic couplings, leading to higher critical temperatures, as emphasized by the recent discovery of superconductivity in nickelates7, 8, 9-10. Quantum simulators with ultracold atoms provide a versatile platform to engineer such couplings and to observe emergent structures in real space with single-particle resolution. Here we show, to our knowledge, the first signatures of individual stripes in a cold-atom Fermi-Hubbard quantum simulator using mixed-dimensional (mixD) settings. Increasing the energy scale of hole-hole attraction to the spin exchange energy, we access the interesting crossover temperature regime in which stripes begin to form11. We observe extended, attractive correlations between hole dopants and find an increased probability of forming larger structures akin to individual stripes. In the spin sector, we study correlation functions up to the third order and find results consistent with stripe formation. These observations are interpreted as a precursor to the stripe phase, which is characterized by interleaved charge and spin density wave ordering with fluctuating lines of dopants separating domains of opposite antiferromagnetic order12, 13-14.

The simulation of high-temperature superconducting materials by implementing strongly correlated fermionic models in optical lattices is one of the major objectives in the field of analog quantum simulation. Here we show that local control and optical bilayer capabilities combined with spatially resolved measurements create a versatile toolbox to study fundamental properties of both nickelate and cuprate high-temperature superconductors. On the one hand, we present a scheme to implement a mixed- dimensional (mixD) bilayer model that has been proposed to capture the essential pairing physics of pressurized bilayer nickelates. This allows for the long-sought realization of a state with long-range superconducting order in current lattice quantum simulation machines. In particular, we show how coherent pairing correlations can be accessed in a partially particle-hole transformed and rotated basis. On the other hand, we demonstrate that control of local gates enables the observation of d-wave pairing order in the two-dimensional (single-layer) repulsive Fermi-Hubbard model through the simulation of a system with attractive interactions. Lastly, we introduce a scheme to measure momentum-resolved dopant densities, providing access to observables complementary to solid-state experiments-which is of particular interest for future studies of the enigmatic pseudogap phase appearing in cuprates.

Lattice gauge theories (LGTs) were introduced in 1974 by Wilson to study quark confinement. These models have been shown to exhibit (de)confined phases, yet it remains challenging to define experimentally accessible order parameters. Here we propose percolation-inspired order parameters (POPs) to probe confinement of dynamical matter in Z(2) LGTs using electric field basis snapshots accessible to quantum simulators. We apply the POPs to study a classical Z(2) LGT and find a confining phase up to temperature T = infinity in two dimensions (critical T-c, i.e., finite-T phase transition, in three dimensions) for any nonzero density of Z(2) charges. Further, using quantum Monte Carlo we demonstrate that the POPs reproduce the square lattice Fradkin-Shenker phase diagram at T = infinity and explore the phase diagram at T > 0. The correlation length exponent coincides with the one of the three-dimensional Ising universality class and we determine the POP critical exponent characterizing percolation. Our proposed POPs provide a geometric perspective of confinement and are directly accessible to snapshots obtained in quantum simulators, making them suitable as a probe for quantum spin liquids.

Ever since the discovery of high-temperature superconductivity in cuprates, gaining microscopic insights into the nature of pairing in strongly correlated systems has remained one of the greatest challenges in modern condensed matter physics. Following recent experiments reporting superconductivity in the bilayer nickelate La3Ni2O7 (LNO) with remarkably high critical temperatures of Tc = 80 K, it has been argued that the low-energy physics of LNO can be described by the strongly correlated, mixed-dimensional bilayer t-J model. Here we investigate this bilayer system and utilize density matrix renormalization group techniques to establish a thorough understanding of the model and the magnetically induced pairing through comparison to the perturbative limit of dominating inter-layer spin couplings. In particular, this allows us to explain appearing finite-size effects, firmly establishing the existence of long-range superconducting order in the thermodynamic limit. By analyzing binding energies, we predict a BEC-BCS crossover as a function of the Hamiltonian parameters. We find large binding energies of the order of the inter-layer coupling that suggest strikingly high critical temperatures of the Berezinskii-Kosterlitz-Thouless transition, raising the question of whether (mixD) bilayer superconductors possibly facilitate critical temperatures above room temperature. The authors study a minimal model to describe the physics of bilayer nickelates, a novel high-temperature superconductor. They find that the model features extraordinarily high critical temperatures for superconductivity, and gain a detailed understanding of the underlying physics through an intuitive perturbative limit.

Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the simulation of such systems, namely neural quantum states (NQS), which overcome the exponential scaling by compressing the state in terms of the network parameters rather than storing all exponentially many coefficients needed for an exact parameterization of the state. We introduce the commonly used NQS architectures and their various applications for the simulation of ground and excited states, finite temperature and open system states as well as NQS approaches to simulate the dynamics of quantum states. Furthermore, we discuss NQS in the context of quantum state tomography.

A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry. Recent advancements in the experimental realizations of large-scale LGTs have been impressive, albeit mostly restricted to Abelian gauge groups. Guided by this requirement for gauge protection, we propose an experimentally feasible approach to implement large-scale non-Abelian SU(N) and U(N) LGTs with dynamical matter in d + 1D, enabled by two-body spin-exchange interactions realizing local emergent gauge-symmetry stabilizer terms. We present two concrete proposals for 2 + 1D SU(2) and U(2) LGTs, including dynamical bosonic matter and induced plaquette terms, that can be readily implemented in current ultracold-molecule and next-generation ultracold-atom platforms. We provide numerical benchmarks showcasing experimentally accessible dynamics, and demonstrate the stability of the underlying non-Abelian gauge invariance. We develop a method to obtain the effective gauge-invariant model featuring the relevant magnetic plaquette and minimal gauge-matter coupling terms. Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators.

The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) t-J model whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground-state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N) Fermi-Hubbard models on various geometries.

A key to understanding unconventional superconductivity lies in unraveling the pairing mechanism of mobile charge carriers in doped antiferromagnets, yielding an effective attraction between charges even in the presence of strong repulsive Coulomb interactions. Here, we study pairing in a mixed-dimensional (mixD) t-J model, featuring robust binding energies-despite dominant repulsive interactions-that are strongly enhanced in the finite doping regime. The single and coupled mixD ladders we study, corresponding to bilayers of width w <= 2, feature a crossover from tightly bound pairs of holes (closed channel) at small repulsion to more spatially extended, correlated pairs of individual holes (open channel) at large repulsion. We derive an effective model for the latter, in which the attraction is mediated by the closed channel, in analogy to atomic Feshbach resonances. Using density matrix renormalization group simulations we reveal a dome of large binding energies at around 30% doping, accompanied by a change of the Fermi surface volume and a crossover from extended to tightly bound hole pairs. Our work provides a microscopic theory of pairing in the doped mixD system with dominant repulsion, closely related to bilayer, Ni-based superconductors, and our predictions can be tested in state-of-theart quantum simulators.

"Modern cosmological research in large-scale structure has witnessed an increasing number of machine-learning applications. Among them, convolutional neural networks (CNNs) have received substantial attention due to their outstanding performance in image classification, cosmological parameter inference, and various other tasks. However, many models based on CNNs are criticized as ""black boxes"" due to the difficulties in relating their outputs intuitively and quantitatively to the cosmological fields under investigation. To overcome this challenge, we present the Cosmological Correlator Convolutional Neural Network (C3NN)-a fusion of CNN architecture and cosmological N-point correlation functions (NPCFs). We demonstrate that its output can be expressed explicitly in terms of the analytically tractable NPCFs. Together with other auxiliary algorithms, we can open the ""black box"" by quantitatively ranking different orders of the interpretable outputs based on their contribution to classification tasks. As a proof of concept, we demonstrate this by applying our framework to a series of binary classification tasks using Gaussian and log-normal random fields and relating its outputs to the NPCFs describing the two fields. Furthermore, we exhibit the model's ability to distinguish different dark energy scenarios (w 0 = -0.95 and -1.05) using N-body simulated weak-lensing convergence maps and discuss the physical implications coming from their interpretability. With these tests, we show that C3NN combines advanced aspects of machine learning architectures with the framework of cosmological NPCFs, thereby making it an exciting tool to extract physical insights in a robust and explainable way from observational data."

Microscopically understanding competing orders in strongly correlated systems is a key challenge in modern quantum many-body physics. For example, the study of magnetic polarons and their relation to pairing in the Fermi-Hubbard model in different geometries remains one of the central questions, and may help to understand the mechanism underlying unconventional superconductivity in cuprates or transition metal dichalcogenides. With recent advances in analog quantum simulation of the Fermi-Hubbard model on nonbipartite lattices, frustrated physics can now be explored experimentally in systems lacking particle-hole symmetry. Here, we study the singly doped t - J model on the triangular lattice, focusing on the competition between kinetic and magnetic frustration as a function of temperature. In doublon doped systems, we uncover a crossover between Nagaoka-type ferromagnetic (FM) correlations at high temperature and exchange mediated antiferromagnetic (AFM) order around the doublon at low temperature. For hole-doped systems, kinetic Haerter-Shastry-type AFM at high temperature as well as exchange interactions at low temperature favor 120 degrees order, strengthening magnetic correlations compared to the undoped system. In the ground state, the presence of AFM correlations throughout a wide range of interactions indicates confinement of both types of dopants. In this regime we firmly establish the presence of linear confining potentials via energy scaling arguments, supporting the picture of geometric strings in the frustrated triangular t - J model.

The combination of optical tweezer arrays with strong interactions-via dipole exchange of molecules and Van der Waals interactions of Rydberg atoms-has opened the door for the exploration of a wide variety of quantum spin models. A next significant step will be the combination of such settings with mobile dopants. This will enable one to simulate the physics believed to underlie many strongly correlated quantum materials. Here, we propose an experimental scheme to realize bosonic t-J models via encoding the local Hilbert space in a set of three internal atomic or molecular states. By engineering antiferromagnetic (AFM) couplings between spins, competition between charge motion and magnetic order similar to that in high-T-c cuprates can be realized. Since the ground states of the 2D bosonic AFM t-J model we propose to realize have not been studied extensively before, we start by analyzing the case of two dopants-the simplest instance in which their bosonic statistics plays a role-and compare our results to the fermionic case. We perform large-scale density matrix renormalization group calculations on six-legged cylinders, and find a strong tendency for bosonic holes to form stripes. This demonstrates that bosonic, AFM t-J models may contain similar physics as the collective phases in strongly correlated electrons.

New generations of ultracold-atom experiments are continually raising the demand for efficient solutions to optimal control problems. Here, we apply Bayesian optimization to improve a state-preparation protocol recently implemented in an ultracold-atom system to realize a two-particle fractional quantum Hall state. Compared to manual ramp design, we demonstrate the superior performance of our optimization approach in a numerical simulation - resulting in a protocol that is 10 x faster at the same fidelity, even when taking into account experimentally realistic levels of disorder in the system. We extensively analyze and discuss questions of robustness and the relationship between numerical simulation and experimental realization, and how to make the best use of the surrogate model trained during optimization. We find that numerical simulation can be expected to substantially reduce the number of experiments that need to be performed with even the most basic transfer learning techniques. The proposed protocol and workflow will pave the way toward the realization of more complex many-body quantum states in experiments.

Numerically simulating large, spinful, fermionic systems is of great interest in condensed matter physics. However, the exponential growth of the Hilbert space dimension with system size renders exact quantum state parameterizations impractical. Owing to their representative power, neural networks often allow to overcome this exponential scaling. Here, we investigate the ability of neural quantum states (NQS) to represent the bosonic and fermionic t - J model - the high interaction limit of the Hubbard model - on various 1D and 2D lattices. Using autoregressive, tensorized recurrent neural networks (RNNs), we study ground state representations upon hole doping the half-filled system. Additionally, we propose a method to calculate quasiparticle dispersions, applicable to any network architecture or lattice geometry, and allowing to infer the low-energy physics from NQS. By analyzing the strengths and weaknesses of the RNN ansatz we shed light on the challenges and promises of NQS for simulating bosonic and fermionic systems. Neural network quantum states (NQS) are a promising method to simulate large fermionic systems. This work reports on accurate simulations of the t-J model in 1D and 2D lattices by means of NQS based on a recurrent neural network (RNN) architecture focusing on the calculation of dispersion relations, for which a general method is introduced, and on the performance of the RNN ansatz upon doping.

We analyze the formation of multiparticle bound states in ladders with frustrated kinetic energy in twocomponent bosonic and two-component fermionic systems. We focus on the regime of light doping relative to insulating states at half-filling, spin polarization close to 100%, and strong repulsive interactions. A special feature of these systems is that the binding energy scales with single-particle tunneling t rather than exchange interactions, since effective attraction arises from alleviating kinetic frustration. For two-component Fermi systems on a zigzag ladder we find a bound state between a hole and a flipped spin (magnon) with a binding energy that can be as large as 0.6t. We demonstrate that magnon-hole attraction leads to formation of clusters comprising several holes and magnons, and we expound on antiferromagentic correlations for the transverse spin components inside the clusters. We identify several many-body states that result from self-organization of multiparticle bound states, including a Luttinger liquid of hole-magnon pairs and a density wave state of two-hole-three-magnon composites. We establish a symmetry between the spectra of Bose and Fermi systems and use it to establish the existence of antibound states in two-component Bose mixtures with SU(2) symmetric repulsion on a zigzag ladder. We also consider Bose and Fermi systems on a square ladder with flux and demonstrate that both systems support bound states. We discuss experimental signatures of multiparticle bound states in both equilibrium and dynamical experiments. We point out intriguing connections between these systems and the quark bag model in QCD.

Topological phase transitions go beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking and occur without an associated local order parameter. Instead, such transitions can be characterized by the emergence of nonlocal order parameters, which require measurements on extensively many particles simultaneously-an impossible venture in real materials. On the other hand, quantum simulators have demonstrated such measurements, making them prime candidates for experimental confirmation of nonlocal topological order. Here, building upon the recent advances in preparing few-particle fractional Chern insulators using ultracold atoms and photons, we propose a realistic scheme for detecting the hidden off-diagonal long-range order (HODLRO) characterizing Laughlin states. Furthermore, we demonstrate the existence of this hidden order in fractional Chern insulators, specifically for the nu = 1/2-Laughlin state in the isotropic Hofstadter-Bose-Hubbard model. This is achieved by large-scale numerical density matrix renormalization group (DMRG) simulations based on matrix product states, for which we formulate an efficient sampling procedure providing direct access to HODLRO in close analogy to the proposed experimental scheme. We confirm the characteristic power-law scaling of HODLRO, with an exponent 1/nu = 2, and show that its detection requires only a few thousand snapshots. This makes our scheme realistically achievable with current technology and paves the way for further analysis of nonlocal topological orders, e.g., in topological states with non-Abelian anyonic excitations.

"When a mobile hole is doped into an antiferromagnet, its movement will distort the surrounding magnetic order and yield a magnetic polaron. The resulting complex interplay of spin and charge degrees of freedom gives rise to very rich physics and is widely believed to be at the heart of high -temperature superconductivity in cuprates. In this paper, we develop a quantitative theoretical formalism, based on the phenomenological parton description, to describe magnetic polarons in the strong -coupling regime. We construct an effective Hamiltonian with weak coupling to the spin -wave excitations in the background, making the use of standard polaronic methods possible. Our starting point is a single hole doped into an antiferromagnet described by a ""geometric string"" capturing the strongly correlated hopping processes of charge and spin degrees of freedom, beyond linear spin -wave approximation. Subsequently, we introduce magnon excitations through a generalized 1 / S expansion and derive an effective coupling of these spin waves to the hole plus the string (the meson) to arrive at an effective polaron Hamiltonian with density -density type interactions. After making a Born-Oppenheimer-type approximation, this system is solved using the self -consistent Born approximation to extract the renormalized polaron properties. We apply our formalism (i) to calculate beyond linear spin -wave angle -resolved photoemission spectroscopy spectra, (ii) to reveal the interplay of rovibrational meson excitations, and (iii) to analyze the pseudogap expected at low doping. Moreover, our work paves the way for exploring magnetic polarons out of equilibrium or in frustrated systems, where weak -coupling approaches are desirable and going beyond linear spin -wave theory becomes necessary."

Programmable quantum simulators based on Rydberg atom arrays are a fast-emerging quantum platform, bringing together long coherence times, high-fidelity operations, and large numbers of interacting qubits deterministically arranged in flexible geometries. Today's Rydberg array devices are demonstrating their utility as quantum simulators for studying phases and phase transitions in quantum matter. In this paper, we show that unprocessed and imperfect experimental projective measurement data can be used to enhance in silico simulations of quantum matter, by improving the performance of variational Monte Carlo simulations. As an example, we focus on data spanning the disordered-to-checkerboard transition in a 16 x 16 square-lattice array [S. Ebadi et al., Nature (London) 595, 227 (2021)] and employ the data-enhanced variational Monte Carlo algorithm to train powerful autoregressive wave-function ansatze based on recurrent neural networks (RNNs). We observe universal improvements in the convergence times of our simulations with this hybrid training scheme. Notably, we also find that pretraining with experimental data enables relatively simple RNN ansatze to accurately capture phases of matter that are not learned with a purely variational training approach. Our work highlights the promise of hybrid quantum-classical approaches for large-scale simulation of quantum many-body systems, combining autoregressive language models with experimental data from existing quantum devices.

Since the discovery of superconductivity in cuprate materials, the minimal ingredients for high-Tc superconductivity have been an outstanding puzzle. Motivated by the recently discovered nickelate bilayer superconductor La3Ni2O7 under pressure, we study a minimal bilayer model, in which, as in La3Ni2O7, interlayer and intralayer magnetic interactions but no interlayer hopping are present: A mixed-dimensional (mixD) t-J model. In the setting of a mixD ladder, we show that the system exhibits a crossover associated with a Feshbach resonance: From a closed-channel-dominated regime of tightly bound bosonic pairs of holes to an open-channel-dominated regime of spatially more extended Cooper pairs. The crossover can be tuned by varying doping, or by a nearest-neighbor Coulomb repulsion V that we include in our model. Using density matrix renormalization group simulations and analytical descriptions of both regimes, we find that the ground state is a Luther-Emery liquid, competing with a density wave of tetraparton plaquettes at commensurate filling delta = 0.5 at large repulsion, and exhibits a pairing dome where binding is facilitated by doping. Our observations can be understood in terms of pairs of correlated spinon-chargon excitations constituting the open channel, which are subject to attractive interactions mediated by the closed channel of tightly bound chargon-chargon pairs. When the closed channel is lowered in energy by doping or tuning V, a Feshbach resonance is realized, associated with a dome in the binding energy. Our predictions can be directly tested in state-of-the art quantum simulators, and we argue that the pairing mechanism we describe may be realized in the nickelate bilayer superconductor La3Ni2O7.

A key step in unraveling the mysteries of materials exhibiting unconventional superconductivity is to understand the underlying pairing mechanism. While it is widely agreed upon that the pairing glue in many of these systems originates from antiferromagnetic spin correlations, a microscopic description of pairs of charge carriers remains lacking. Here we use state-of-the art numerical methods to probe the internal structure and dynamical properties of pairs of charge carriers in quantum antiferromagnets in four-legged cylinders. Exploiting the full momentum resolution in our simulations, we are able to distinguish two qualitatively different types of bound states: a highly mobile, meta-stable pair, which has a dispersion proportional to the hole hopping t, and a heavy pair, which can only move due to spin exchange processes and turns into a flat band in the Ising limit of the model. Understanding the pairing mechanism can on the one hand pave the way to boosting binding energies in related models, and on the other hand enable insights into the intricate competition of various phases of matter in strongly correlated electron systems.

Recently, tremendous progress has been made in the field of quantum science and technologies: different platforms for quantum simulation as well as quantum computing, ranging from superconduct-ing qubits to neutral atoms, are start-ing to reach unprecedentedly large sys-tems. In order to benchmark these sys-tems and gain physical insights, the need for efficient tools to characterize quantum states arises. The exponential growth of the Hilbert space with system size ren-ders a full reconstruction of the quantum state prohibitively demanding in terms of the number of necessary measurements. Here we propose and implement an ef-ficient scheme for quantum state tomog-raphy using active learning. Based on a few initial measurements, the active learn-ing protocol proposes the next measure-ment basis, designed to yield the max-imum information gain. We apply the active learning quantum state tomogra-phy scheme to reconstruct different multi-qubit states with varying degree of entan-glement as well as to ground states of the XXZ model in 1D and a kinetically con-strained spin chain. In all cases, we obtain a significantly improved reconstruction as compared to a reconstruction based on the exact same number of measurements and measurement configurations, but with ran-domly chosen basis configurations. Our scheme is highly relevant to gain physical insights in quantum many-body systems as well as for benchmarking and character-izing quantum devices, e.g. for quantum simulation, and paves the way for scalable adaptive protocols to probe, prepare, and manipulate quantum systems.

Microscopically understanding and classifying phases of matter is at the heart of strongly-correlated quantum physics. With quantum simulations, genuine projective measurements (snapshots) of the many-body state can be taken, which include the full information of correlations in the system. The rise of deep neural networks has made it possible to routinely solve abstract processing and classification tasks of large datasets, which can act as a guiding hand for quantum data analysis. However, though proven to be successful in differentiating between different phases of matter, conventional neural networks mostly lack interpretability on a physical footing. Here, we combine confusion learning [1] with correlation convolutional neural networks [2], which yields fully interpretable phase detection in terms of correlation functions. In particular, we study thermodynamic properties of the 2D Heisenberg model, whereby the trained network is shown to pick up qualitative changes in the snapshots above and below a characteristic temperature where magnetic correlations become significantly long-range. We identify the full counting statistics of nearest neighbor spin correlations as the most important quantity for the decision process of the neural network, which go beyond averages of local observables. With access to the fluctuations of second-order correlations - which indirectly include contributions from higher order, long-range correlations - the network is able to detect changes of the specific heat and spin susceptibility, the latter being in analogy to magnetic properties of the pseudogap phase in high-temperature superconductors [3]. By combining the confusion learning scheme with transformer neural networks, our work opens new directions in interpretable quantum image processing being sensible to long-range order.

Unveiling the microscopic origins of quantum phases dominated by the interplay of spin and motional degrees of freedom constitutes one of the central challenges in strongly correlated many-body physics. When holes move through an antiferromagnetic spin background, they displace the positions of spins, which induces effective frustration in the magnetic environment. However, a concrete characterization of this effect in a quantum many-body system is still an unsolved problem. Here we present a Hamiltonian reconstruction scheme that allows for a precise quantification of hole-motion-induced frustration. We access non-local correlation functions through projective measurements of the many-body state, from which effective spin-Hamiltonians can be recovered after detaching the magnetic background from dominant charge fluctuations. The scheme is applied to systems of mixed dimensionality, where holes are restricted to move in one dimension, but SU(2) superexchange is two-dimensional. We demonstrate that hole motion drives the spin background into a highly frustrated regime, which can quantitatively be described by an effective J(1)-J(2)-type spin model. We exemplify the applicability of the reconstruction scheme to ultracold atom experiments by recovering effective spin-Hamiltonians of experimentally obtained 1D Fermi-Hubbard snapshots. Our method can be generalized to fully 2D systems, enabling promising microscopic perspectives on the doped Hubbard model.

Gauge fields coupled to dynamical matter are ubiquitous in many disciplines of physics, ranging from particle to condensed matter physics, but their implementation in large-scale quantum simulators remains challenging. Here we propose a realistic scheme for Rydberg atom array experiments in which a Z2 gauge structure with dynamical charges emerges on experimentally relevant timescales from only local two-body interactions and one-body terms in two spatial dimensions. The scheme enables the experimental study of a variety of models, including (2+ 1)D Z2 lattice gauge theories coupled to different types of dynamical matter and quantum dimer models on the honeycomb lattice, for which we derive effective Hamiltonians. We discuss ground-state phase diagrams of the experimentally most relevant effective Z2 lattice gauge theories with dynamical matter featuring various confined and deconfined, quantum spin liquid phases. Further, we present selected probes with immediate experimental relevance, including signatures of disorder-free localization and a thermal deconfinement transition of two charges.

Quantum many-body scarring is a paradigm of weak ergodicity breaking arising due to the presence of special nonthermal many-body eigenstates that possess low entanglement entropy, are equally spaced in energy, and concentrate in certain parts of the Hilbert space. Though scars have been shown to be intimately connected to gauge theories, their stability in such experimentally relevant models is still an open question, and it is generally considered that they exist only under fine-tuned conditions. In this work, we show through Krylov-based time-evolution methods how quantum many-body scars can be made robust in the presence of experimental errors through utilizing terms linear in the gaugesymmetry generator or a simplified pseudogenerator in U(1) and Z2 lattice gauge theories. Our findings are explained by the concept of quantum Zeno dynamics. Our experimentally feasible methods can be readily implemented in existing large-scale ultracold-atom quantum simulators and setups of Rydberg atoms with optical tweezers.

In strongly correlated quantum materials, the behavior of charge carriers is dominated by strong electron-electron interactions. These can lead to insulating states with spin order, and upon doping to competing ordered states including unconventional super-conductivity. The underlying pairing mechanism remains poorly understood however, even in strongly simplified theoretical models. Recent advances in quantum simulation allow to study pairing in paradigmatic settings, e.g. in the t - J and t - Jz Hamiltoni-ans. Even there, the most basic properties of paired states of only two dopants, such as their dispersion relation and excitation spectra, remain poorly studied in many cases. Here we provide new analytical insights into a possible string-based pairing mechanism of mobile holes in an antiferromagnet. We analyze an effective model of partons con-nected by a confining string and calculate the spectral properties of bound states. Our model is equally relevant for understanding Hubbard-Mott excitons consisting of a bound doublon-hole pair or confined states of dynamical matter in lattice gauge theories, which motivates our study of different parton statistics. Although an accurate semi-analytic es-timation of binding energies is challenging, our theory provides a detailed understanding of the internal structure of pairs. For example, in a range of settings we predict heavy states of immobile pairs with flat-band dispersions - including for the lowest-energy d -wave pair of fermions. Our findings shed new light on the long-standing question about the origin of pairing and competing orders in high-temperature superconductors.

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.

Preparing finite-temperature states in quantum simulators of spin systems, such as trapped ions or Rydberg atoms in optical tweezers, is challenging due to their almost perfect isolation from the environment. Here, we show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality and equivalent to the one in Lu et al., PRX Quantum 2, 020321 (2021). It consists of classical importance sampling of initial states and a measurement of the Loschmidt echo with a quantum simulator. We use the method as a quantum-inspired classical algorithm and simulate the protocol with matrix product states to analyze the requirements on a quantum simulator. This way, we show that a finite-temperature phase transition in the long-range transverse-field Ising model can be characterized in trapped ion quantum simulators. We propose a concrete measurement protocol for the Loschmidt echo and discuss the influence of measurement noise, dephasing, as well as state preparation and measurement errors. We argue that the algorithm is robust against those imperfections under realistic conditions.

Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions' dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter-Fermi-Hubbard model using ultracold atoms. We demonstrate, by performing large-scale density-matrix renormalization group simulations, that this model exhibits a lattice analog of the quantum Hall (QH) ferromagnet at magnetic filling factor nu = 1. We reveal the nature of the low energy spin-singlet states around nu asymptotic to 1 and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice QH ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high- T-c superconductivity.

It is a widely accepted view that the interplay of spin and charge degrees of freedom in doped antiferromagnets (AFMs) gives rise to the rich physics of high-temperature superconductors. Nevertheless, it remains unclear how effective low-energy degrees of freedom and the corresponding field theories emerge from microscopic models, including t - J and Hubbard Hamiltonians. A promising view comprises that the charge carriers have a rich internal parton structure on intermediate scales, but the interplay of the emergent partons with collective magnon excitations of the surrounding AFM remains unexplored. Here we study a doped one-dimensional spin chain in a staggered magnetic field and demonstrate that it supports a zoo of various long-lived excitations. These include magnons, mesonic pairs of spinons and chargons along with their rovibrational excitations, and tetraparton bound states of mesons and magnons. We identify these types of quasiparticles in various spectra using density-matrix renormalization group simulations. Moreover, we introduce a strong-coupling theory describing the polaronic dressing and molecular binding of mesons to collective magnon excitations. The effective theory can be solved by standard tools developed for polaronic problems and can be extended to study similar physics in two-dimensional doped AFMs in the future. Experimentally, the doped spin-chain in a staggered field can be directly realized in quantum gas microscopes.

Conventional superconductivity emerges from pairing of charge carriers-electrons or holes-mediated by phonons(1). In many unconventional superconductors, the pairing mechanism is conjectured to be mediated by magnetic correlations(2), as captured by models of mobile charges in doped antiferromagnets(3). However, a precise understanding of the underlying mechanism in real materials is still lacking and has been driving experimental and theoretical research for the past 40 years. Early theoretical studies predicted magnetic-mediated pairing of dopants in ladder systems(4-8), in which idealized theoretical toy models explained how pairing can emerge despite repulsive interactions(9). Here we experimentally observe this long-standing theoretical prediction, reporting hole pairing due to magnetic correlations in a quantum gas of ultracold atoms. By engineering doped antiferromagnetic ladders with mixed-dimensional couplings(10), we suppress Pauli blocking of holes at short length scales. This results in a marked increase in binding energy and decrease in pair size, enabling us to observe pairs of holes predominantly occupying the same rung of the ladder. We find a hole-hole binding energy of the order of the superexchange energy and, upon increased doping, we observe spatial structures in the pair distribution, indicating repulsion between bound hole pairs. By engineering a configuration in which binding is strongly enhanced, we delineate a strategy to increase the critical temperature for superconductivity.

Experimental realizations of topologically ordered states of matter, such as fractional quantum Hall states, with cold atoms are now within reach. In particular, optical lattices provide a promising platform for the realization and characterization of such states, where novel detection schemes enable an unprecedented microscopic under-standing. Here we show that the central charge can be directly measured in current cold atom experiments using the number entropy as a proxy for the entanglement entropy. We perform density-matrix renormalization-group simulations of Hubbard-interacting bosons on coupled chains subject to a magnetic field with alpha = 1/4 flux quanta per plaquette. Tuning the interchain hopping, we find a transition from a trivial quasi-one-dimensional phase to the topologically ordered Laughlin state at magnetic filling factor nu = 1/2 for systems of three or more chains. We resolve the transition using the central charge, on-site correlations, momentum distributions, and the many-body Chern number. Additionally, we propose a scheme to experimentally estimate the central charge from Fock basis snapshots. The model studied here is experimentally realizable with existing cold atom techniques and the proposed observables pave the way for the detection and classification of a larger class of interacting topological states of matter.

In strongly interacting systems with a separation of energy scales, low-energy effective Hamiltonians help provide insights into the relevant physics at low temperatures. The emergent interactions in the effective model are mediated by virtual excitations of high-energy states: For example, virtual doublon-hole excitations in the Fermi-Hubbard model mediate antiferromagnetic spin-exchange interactions in the derived effective model, known as the t - J - 3s model. Formally this procedure is described by performing a unitary Schrieffer-Wolff basis transformation. In the context of quantum simulation, it can be advantageous to consider the effective model to interpret experimental results. However, virtual excitations such as doublon-hole pairs can obfuscate the measurement of physical observables. Here we show that quantum simulators allow one to access the effective model even more directly by performing measurements in a rotated basis. We propose a protocol to perform a Schrieffer-Wolff transformation on Fermi-Hubbard low-energy eigenstates (or thermal states) to dynamically prepare approximate t - J - 3s model states using fermionic atoms in an optical lattice. Our protocol involves performing a linear ramp of the optical lattice depth, which is slow enough to eliminate the virtual doublon-hole fluctuations but fast enough to freeze out the dynamics in the effective model. We perform a numerical study using exact diagonalization and find an optimal ramp speed for which the state after the lattice ramp has maximal overlap with the t - J - 3s model state. We compare our numerics to experimental data from our Lithium-6 fermionic quantum gas microscope and show a proof-of-principle demonstration of this protocol. More generally, this protocol can be beneficial to studies of effective models by enabling the suppression of virtual excitations in a wide range of quantum simulation experiments.

The mechanism underlying charge transport in strongly correlated quantum systems, such as doped antiferromagnetic Mott insulators, remains poorly understood. Here, we study the expansion dynamics of an initially localized hole inside a two-dimensional (2D) Ising antiferromagnet at variable temperature. Using a combination of classical Monte Carlo and truncated-basis methods, we reveal two dynamically distinct regimes: a spin-charge confined region below a critical temperature T*, characterized by slow spreading, and a spin-charge deconfined region above T*, characterized by an unbounded diffusive expansion. The deconfinement temperature T* ti 0.65Jz we find is around the N??el temperature TN = 0.567Jz of the Ising background in 2D, but we expect T* < TN in higher dimensions. In both regimes we find that the mobile hole does not thermalize with the Ising spin background on the considered time scales, indicating weak effective coupling of spin and charge degrees of freedom. Our results can be qualitatively understood by an effective parton model and can be tested experimentally in state-of-the-art quantum gas microscopes.

Realizing and characterizing interacting topological phases in synthetic quantum systems is a formidable challenge. Here, we propose a Floquet protocol to realize the antiferromagnetic Heisenberg model with power -law decaying interactions. Based on analytical and numerical arguments, we show that this model features a quantum phase transition from a liquid to a valence bond solid that spontaneously breaks lattice translational symmetry and is reminiscent of the Majumdar-Ghosh state. The different phases can be probed dynamically by measuring the evolution of a fully dimerized state. We moreover introduce an interferometric protocol to characterize the topological excitations and the bulk topological invariants of the interacting many-body system.

Studies of unconventional pairing mechanisms in cold atoms require ultralow temperatures. Large-scale numerics show that certain bilayer models allow for deeply bound and highly mobile pairs of charges at more accessible temperatures. Interacting many-body systems in reduced-dimensional settings, such as ladders and few-layer systems, are characterized by enhanced quantum fluctuations. Recently, two-dimensional bilayer systems have sparked considerable interest because they can host unusual phases, including unconventional superconductivity. Here we present a theoretical proposal for realizing high-temperature pairing of fermions in a class of bilayer Hubbard models. We introduce a general and highly efficient pairing mechanism for mobile charge carriers in doped antiferromagnetic Mott insulators. The pairing is caused by the energy that one charge gains when it follows the path created by another charge. We show that this mechanism leads to the formation of highly mobile but tightly bound pairs in the case of mixed-dimensional Fermi-Hubbard bilayer systems. This setting is closely related to the Fermi-Hubbard model believed to capture the physics of copper oxides, and can be realized in currently available ultracold atom experiments.

Disorder-free localization is a recently discovered phenomenon of nonergodicity that can emerge in quantum many-body systems hosting gauge symmetries when the initial state is prepared in a superposition of gauge superselection sectors. Thermalization is then prevented up to all accessible evolution times despite the model being nonintegrable and translation invariant. In a recent work [Halimeh et al., arXiv:2111.02427 (2021)], it has been shown that terms linear in the gauge-symmetry generator stabilize disorder-free localization in U(1) gauge theories against gauge errors that couple different superselection sectors. Here, we show in the case of Z2 gauge theories that disorder-free localization can not only be stabilized, but also enhanced by the addition of translation-invariant terms linear in a local Z2 pseudogenerator that acts identically to the full generator in a single superselection sector, but not necessarily outside of it. We show analytically and numerically how this leads through the quantum Zeno effect to the dynamical emergence of a renormalized gauge theory with an enhanced local symmetry, which contains the Z2 gauge symmetry of the ideal model, associated with the Z2 pseudogenerator. The resulting proliferation of superselection sectors due to this dynamically emergent gauge theory creates an effective disorder greater than that in the original model, thereby enhancing disorder-free localization. We demonstrate the experimental feasibility of the Z2 pseudogenerator by providing a detailed readily implementable experimental proposal for the observation of disorder-free localization in a Rydberg setup.

The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase of matter. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth,. they commonly result in slow and subtle modifications of the dynamics, rendering their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two-qubit density matrices allows us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here detect affirmative quantum correlations and exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter.

Quantum simulation experiments have started to explore regimes that are not accessible with exact numerical methods. To probe these systems and enable new physical insights, the need for measurement protocols arises that can bridge the gap to solid-state experiments, and at the same time make optimal use of the capabilities of quantum simulation experiments. Here we propose applying time-dependent photoemission spectroscopy, an established tool in solid-state systems, in cold atom quantum simulators. Concretely, we suggest combining the method with large magnetic field gradients, unattainable in experiments on real materials, to drive Bloch oscillations of spinons, the emergent quasiparticles of spin liquids. We show in exact diagonalization simulations of the one-dimensional t-J model with a single hole that the spinons start to populate previously unoccupied states in an effective band structure, thus allowing us to visualize states invisible in the equilibrium spectrum. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons. In numerical simulations of small two-dimensional systems, spectral weight appears at the ground-state energy at momentum q = (pi, pi), where the equilibrium spectral response is strongly suppressed up to higher energies, indicating a possible route toward solving the mystery of the Fermi arcs in the cuprate materials.

In the last decade, quantum simulators, and in particular cold atoms in optical lattices, have emerged as a valuable tool to study strongly correlated quantum matter. These experiments are now reaching regimes that are numerically difficult or impossible to access. In particular they have started to fulfill a promise which has contributed significantly to defining and shaping the field of cold atom quantum simulations, namely the exploration of doped and frustrated quantum magnets and the search for the origins of high-temperature superconductivity in the fermionic Hubbard model. Despite many future challenges lying ahead, such as the need to further lower the experimentally accessible temperatures, remarkable studies have already been conducted. Among them, spin-charge separation in one-dimensional systems has been demonstrated, extended-range antiferromagnetism in two-dimensional systems has been observed, connections to modern day large-scale numerical simulations were made, and unprecedented comparisons with microscopic trial wavefunctions have been carried out at finite doping. In many regards, the field has acquired new realms, putting old ideas to a new test and producing new insights and inspiration for the next generation of physicists. In the first part of this paper, we review the results achieved in cold atom realizations of the Fermi-Hubbard model in recent years. We put special emphasis on the new probes available in quantum gas microscopes, such as higher-order correlation functions, full counting statistics, the ability to study far-from -equilibrium dynamics, machine learning and pattern recognition of instantaneous snapshots of the many-body wavefunction, and access to non-local correlators. Our review is written from a theoretical perspective, but aims to provide basic understanding of the experimental procedures. We cover one- dimensional systems, where the phenomenon of spin-charge separation is ubiquitous, and two-dimensional systems where we distinguish between situations with and without doping. Throughout, we focus on the strong coupling regime where the Hubbard inter-actions U dominate and connections to t - J models can be justified. In the second part of this paper, with the stage set and the current state of the field in mind, we propose a new direction for cold atoms to explore: namely mixed-dimensional bilayer systems, where the charge motion is restricted to individual layers which remain coupled through spin-exchange. These systems can be directly realized experimentally and we argue that they have a rich phase diagram, potentially including a strongly correlated BEC-to-BCS cross-over and regimes with different superconducting order parameters, as well as complex parton phases and possibly even analogs of tetraquark states. In particular, we propose a novel, strong pairing mechanism in these systems, which puts the formation of hole pairs at experimentally accessible, elevated temperatures within reach. Ultimately we propose to explore how the physics of the mixed-dimensional bilayer system can be connected to the rich phenomenology of the single-layer Hubbard model. (C) 2021 Elsevier Inc. All rights reserved.

Understanding the nature of charge carriers in doped Mott insulators holds the key to unravelling puzzling properties of strongly correlated electron systems, including cuprate superconductors. Several theoretical models suggested that dopants can be understood as bound states of partons, the analogues of quarks in high-energy physics. However, direct signatures of spinon-chargon bound states are lacking, both in experiment and theory. Here we propose a rotational variant of angle-resolved photo-emission spectroscopy (ARPES) and calculate rotational spectra numerically using the density-matrix renormalization group. We identify long-lived rotational resonances for an individual dopant, which we interpret as a direct indicator of the microscopic structure of spinon-chargon bound states. Similar to Regge trajectories reflecting the quark structure of mesons, we establish a linear dependence of the rotational energy on the superexchange coupling. The rotational peaks we find are strongly suppressed in standard ARPES spectra, but we suggest a multiphoton extension of ARPES which allows us to access rotational spectra. Our findings suggest that multiphoton spectroscopy experiments should provide new insights into emergent universal features of strongly correlated electron systems.

Current quantum simulation experiments are starting to explore nonequilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and timescales. Therefore, the question emerges as to which observables are best suited to study the dynamics in such quantum many-body systems. Using machine learning techniques, we investigate the dynamics and, in particular, the thermalization behavior of an interacting quantum system that undergoes a nonequilibrium phase transition from an ergodic to a many-body localized phase. We employ supervised and unsupervised training methods to distinguish nonequilibrium from equilibrium data, using the network performance as a probe for the thermalization behavior of the system. We test our methods with experimental snapshots of ultracold atoms taken with a quantum gas microscope. Our results provide a path to analyze highly entangled large-scale quantum states for system sizes where numerical calculations of conventional observables become challenging.

The competition between antiferromagnetism and hole motion in two-dimensional Mott insulators lies at the heart of a doping-dependent transition from an anomalous metal to a conventional Fermi liquid. We observe such a crossover in Fermi-Hubbard systems on a cold-atom quantum simulator and reveal the transformation of multipoint correlations between spins and holes upon increasing doping at temperatures around the superexchange energy. Conventional observables, such as spin susceptibility, are furthermore computed from the microscopic snapshots of the system. Starting from a magnetic polaron regime, we find the system evolves into a Fermi liquid featuring incommensurate magnetic fluctuations and fundamentally altered correlations. The crossover is completed for hole dopings around 30%. Our work benchmarks theoretical approaches and discusses possible connections to lowertemperature phenomena.

Analysis of higher-order correlation functions has become a powerful tool for investigating interacting many-body systems in quantum simulators, such as quantum gas microscopes. Experimental measurements of mixed spin-charge correlation functions in the 2D Hubbard have been used to study equilibrium properties of magnetic polarons and to identify coherent and incoherent regimes of their dynamics. In this paper we consider theoretically an extension of this technique to systems which use a pinning potential to reduce the mobility of a single dopant in the Mott insulating regime of the 2D Hubbard model. We find that localization of the dopant has a dramatic effect on its magnetic dressing. The connected third order spin correlations are weakened in the case of a mobile hole but strengthened near an immobile hole. In the case of the fifth-order correlation function, we find that its bare value has opposite signs in cases of the mobile and of fully pinned dopant, whereas the connected part is similar for both cases. We study suppression of higher-order correlators by thermal fluctuations and demonstrate that they can be observed up to temperatures comparable to the spin-exchange energy J. We discuss implications of our results for understanding the interplay of spin and charge in doped Mott insulators.

Image-like data from quantum systems promises to offer greater insight into the physics of correlated quantum matter. However, the traditional framework of condensed matter physics lacks principled approaches for analyzing such data. Machine learning models are a powerful theoretical tool for analyzing image-like data including many-body snapshots from quantum simulators. Recently, they have successfully distinguished between simulated snapshots that are indistinguishable from one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from such approaches. Here, we develop a set of nonlinearities for use in a neural network architecture that discovers features in the data which are directly interpretable in terms of physical observables. Applied to simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, we uncover that the key distinguishing features are fourth-order spin-charge correlators. Our approach lends itself well to the construction of simple, versatile, end-to-end interpretable architectures, thus paving the way for new physical insights from machine learning studies of experimental and numerical data. Physical principles underlying machine learning analysis of quantum gas microscopy data are not well understood. Here the authors develop a neural network based approach to classify image data in terms of multi-site correlation functions and reveal the role of fourth-order correlations in the Fermi-Hubbard model.

Understanding the interplay between charge and spin and its effects on transport is a ubiquitous challenge in quantum many-body systems. In the Fermi-Hubbard model, this interplay is thought to give rise to magnetic polarons, whose dynamics may explain emergent properties of quantum materials such as high-temperature superconductivity. In this work, we use a cold-atom quantum simulator to directly observe the formation dynamics and subsequent spreading of individual magnetic polarons. Measuring the density- and spin-resolved evolution of a single hole in a 2D Hubbard insulator with short-range antiferromagnetic correlations reveals fast initial delocalization and a dressing of the spin background, indicating polaron formation. At long times, we find that dynamics are slowed down by the spin exchange time, and they are compatible with a polaronic model with strong density and spin coupling. Our work enables the study of out-of-equilibrium emergent phenomena in the Fermi-Hubbard model, one dopant at a time.

Traditionally, one- and two-point correlation functions are used to characterize many-body systems. In strongly correlated quantum materials, such as the doped 2D Fermi-Hubbard system, these may no longer be sufficient, because higher-order correlations are crucial to understanding the character of the many-body system and can be numerically dominant. Experimentally, such higher-order correlations have recently become accessible in ultracold atom systems. Here, we reveal strong non-Gaussian correlations in doped quantum antiferromagnets and show that higher-order correlations dominate over lower-order terms. We study a single mobile hole in the t - J model using the density matrix renormalization group and reveal genuine fifth-order correlations which are directly related to the mobility of the dopant. We contrast our results to predictions using models based on doped quantum spin liquids which feature significantly reduced higher-order correlations. Our predictions can be tested at the lowest currently accessible temperatures in quantum simulators of the 2D Fermi-Hubbard model. Finally, we propose to experimentally study the same fifth-order spin-charge correlations as a function of doping. This will help to reveal the microscopic nature of charge carriers in the most debated regime of the Hubbard model, relevant for understanding high-T-c superconductivity.

Tremendous recent progress in the quantum simulation of the Hubbard model paves the way to controllably study doped antiferromagnetic Mott insulators. Motivated by these experimental advancements, we numerically study the real-time dynamics of a single hole created in an antiferromagnet on a square lattice, as described by the t-J model. Initially, the hole spreads ballistically with a velocity proportional to the hopping matrix element. At intermediate to long times, the dimensionality as well as the spin background determine the hole dynamics. A hole created in the ground state of a two dimensional (2D) quantum antiferromagnet propagates again ballistically at long times but with a velocity proportional to the spin exchange coupling, showing the formation of a magnetic polaron. We provide an intuitive explanation of this dynamics in terms of a parton construction, which leads to a good quantitative agreement with the numerical tensor network state simulations. In the limit of infinite temperature and no spin exchange couplings, the dynamics can be approximated by a quantum random walk on a Bethe lattice with coordination number z x303,. 4 Adding Ising interactions corresponds to an effective disordered potential, which can dramatically slow down the hole propagation, consistent with subdiffusive dynamics. The study of the hole dynamics paves the way for understanding the microscopic constituents of this strongly correlated quantum state.

Angle-resolved photoemission spectroscopy (ARPES) has revealed peculiar properties of mobile dopants in correlated antiferromagnets (AFMs). But, describing them theoretically, even in simplified toy models, remains a challenge. Here, we study ARPES spectra of a single mobile hole in the t-J model. Recent progress in the microscopic description of mobile dopants allows us to use a geometric decoupling of spin and charge fluctuations at strong couplings, from which we conjecture a one-to-one relation of the one-dopant spectral function and the spectrum of a constituting spinon in the undoped parent AFM. We thoroughly test this hypothesis for a single hole doped into a two-dimensional Heisenberg AFM by comparing our semianalytical predictions to previous quantum Monte Carlo results and our large-scale time-dependent matrix product state calculations of the spectral function. Our conclusion is supported by a microscopic trial wave function describing spinon-chargon bound states, which captures the momentum and t/J dependence of the quasiparticle residue. From our conjecture we speculate that ARPES measurements in the pseudogap phase of cuprates may directly reveal the Dirac-fermion nature of the constituting spinons. Specifically, we demonstrate that our trial wave function provides a microscopic explanation for the sudden drop of spectral weight around the nodal point associated with the formation of Fermi arcs, assuming that additional frustration suppresses long-range AFM ordering. We benchmark our results by studying the crossover from two to one dimension, where spinons and chargons are confined and deconfined, respectively.

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t - J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.

Dominant multiparticle interactions can give rise to exotic physical phases with anyonic excitations and phase transitions without local order parameters. In spin systems with a global SU(N) symmetry, cyclic ring-exchange couplings constitute the first higher-order interaction in this class. In this Letter, we propose a protocol showing how SU(N)-invariant multibody interactions can he implemented in optical tweezer arrays. We utilize the flexibility to rearrange the tweezer configuration on short timescales compared to the typical lifetimes, in combination with strong nonlocal Rydberg interactions. As a specific example, we demonstrate how a chiral cyclic ring-exchange Hamiltonian can be implemented in a two-leg ladder geometry. We study its phase diagram using density-matrix renormalization group simulations and identify phases with dominant vector chirality, a ferromagnet, and an emergent spin-1 Haldane phase. We also discuss how the proposed protocol can he utilized to implement the strongly frustrated J-Q model, a candidate for hosting a deconfined quantum critical point.

Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.

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.

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.

The interplay of spin and charge degrees of freedom, introduced by doping mobile holes into a Mott insulator with strong antiferromagnetic (AFM) correlations, is at the heart of strongly correlated matter such as high-T-C cuprate superconductors. Here, we capture this interplay in the strong coupling regime and propose a trial wave function of mobile holes in an AFM. Our method provides a microscopic justification for a class of theories which describe doped holes moving in an AFM environment as mesonlike bound states of spinons and chargons. We discuss a model of such bound states from the perspective of geometric strings, which describe a fluctuating lattice geometry introduced by the fast motion of the chargon, relative to the spinon. This is demonstrated to give rise to short-range hidden string order, signatures of which have recently been revealed by ultracold atom experiments at elevated temperatures. We present evidence for such short-range hidden string correlations also at zero temperature by performing numerical density-matrix renormalization-group simulations. To test our microscopic approach, we calculate the ground-state energy and dispersion relation of a hole in an AFM, as well as the magnetic polaron radius, and obtain good quantitative agreement with advanced numerical simulations at strong coupling. We discuss extensions of our analysis to systems without long-range AFM order to systems with short-range magnetic correlations.