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We study the dynamics of hard-core bosons on ladders, in the presence of strong kinetic constrains akin to those of the Bariev model. We use a combination of analytical methods and numerical simulations to establish the phase diagram of the model. The model displays a paired Tomonaga-Luttinger liquid phase featuring an emergent dipole symmetry, which encodes the local pairing constraint into a global, non-local quantity. We scrutinize the effect of such emergent low-energy symmetry during quench dynamics including single particle defects. We observe that, despite being approximate, the dipole symmetry still leads to very slow relaxation dynamics, which we model via an effective field theory. The model we discuss is amenable to realization in both cold atoms in optical lattices and Rydberg atom arrays with dynamics taking place solely in the Rydberg manifold. We present a blueprint protocol to observe the effect of emergent dipole symmetry in such experimental platforms, combining adiabatic state preparation with quench dynamics., Comment: 29 pages, 12 figures

We study nonequilibrium quantum dynamics of spin chains by employing principal component analysis (PCA) on data sets of wave function snapshots and examine how information propagates within these data sets. The quantities we employ are derived from the spectrum of the sample second moment matrix, built directly from data sets. Our investigations on several interacting spin chains featuring distinct spin or energy transport reveal that the growth of data information spreading follows the same dynamical exponents as that of the underlying quantum transport of spin or energy. Specifically, our approach enables an easy, data-driven, and importantly interpretable diagnostic to track energy transport with a limited number of samples, which is usually challenging without any assumption on the Hamiltonian form. These observations are obtained at a modest finite size and evolution time, which aligns with experimental and numerical constraints. Our framework directly applies to experimental quantum simulator data sets of dynamics in higher-dimensional systems, where classical simulation methods usually face significant limitations and apply equally to both near- and far-from-equilibrium quenches., Comment: 10 pages, 6 figures

Recent breakthrough experiments have demonstrated how it is now possible to explore the dynamics of quantum Hall states interacting with quantum electromagnetic cavity fields. While the impact of strongly coupled non-local cavity modes on integer quantum Hall physics has been recently addressed, its effects on fractional quantum Hall (FQH) liquids -- and, more generally, fractionalized states of matter -- remain largely unexplored. In this work, we develop a theoretical framework for the understanding of FQH states coupled to quantum light. In particular, combining analytical arguments with tensor network simulations, we study the dynamics of a $\nu=1/3$ Laughlin state in a single-mode cavity with finite electric field gradients. We find that the topological signatures of the FQH state remain robust against the non-local cavity vacuum fluctuations, as indicated by the endurance of the quantized Hall resistivity. The entanglement spectra, however, carry direct fingerprints of light-matter entanglement and topology, revealing peculiar polaritonic replicas of the $U(1)$ counting. As a further response to cavity fluctuations, we also find a squeezed FQH geometry, encoded in long-wavelength correlations. We additionally observe that moving to strong cavity field gradients leads to an instability towards a sliding Tomonaga-Luttinger liquid phase, featuring a strong density modulation in the gradient direction. Finally, by exploring the low-energy excited spectrum inside the FQH phase, we identify a new quasiparticle, the graviton-polariton, arising from the hybridization between quadrupolar FQH collective excitations (known as gravitons) and light. We discuss the experimental implications of our findings and possible extension of our results to more complex scenarios., Comment: 26 pages, 11 figures. Comments are welcome

In this paper, we investigate the relationship between entanglement and non-stabilizerness (also known as magic) in matrix product states (MPSs). We study the relation between magic and the bond dimension used to approximate the ground state of a many-body system in two different contexts: full state of magic and mutual magic (the non-stabilizer analogue of mutual information, thus free of boundary effects) of spin-1 anisotropic Heisenberg chains. Our results indicate that obtaining converged results for non-stabilizerness is typically considerably easier than entanglement. For full state magic at critical points and at sufficiently large volumes, we observe convergence with $1/\chi^2$, with $\chi$ being the MPS bond dimension. At small volumes, magic saturation is so quick that, within error bars, we cannot appreciate any finite-$\chi$ correction. Mutual magic also shows a fast convergence with bond dimension, whose specific functional form is however hindered by sampling errors. As a by-product of our study, we show how Pauli-Markov chains (originally formulated to evaluate magic) resets the state of the art in terms of computing mutual information for MPS. We illustrate this last fact by verifying the logarithmic increase of mutual information between connected partitions at critical points. By comparing mutual information and mutual magic, we observe that, for connected partitions, the latter is typically scaling much slower - if at all - with the partition size, while for disconnected partitions, both are constant in size., Comment: 12 pages, 13 figures

Nonstabilizerness, also known as ``magic'', stands as a crucial resource for achieving a potential advantage in quantum computing. Its connection to many-body physical phenomena is poorly understood at present, mostly due to a lack of practical methods to compute it at large scales. We present a novel approach for the evaluation of nonstabilizerness within the framework of matrix product states (MPS), based on expressing the MPS directly in the Pauli basis. Our framework provides a powerful tool for efficiently calculating various measures of nonstabilizerness, including stabilizer R\'enyi entropies, stabilizer nullity, and Bell magic, and enables the learning of the stabilizer group of an MPS. We showcase the efficacy and versatility of our method in the ground states of Ising and XXZ spin chains, as well as in circuits dynamics that has recently been realized in Rydberg atom arrays, where we provide concrete benchmarks for future experiments on logical qubits up to twice the sizes already realized., Comment: 7+10 pages, 3+7 figures

We introduce a method to measure many-body magic in quantum systems based on a statistical exploration of Pauli strings via Markov chains. We demonstrate that sampling such Pauli-Markov chains gives ample flexibility in terms of partitions where to sample from: in particular, it enables to efficiently extract the magic contained in the correlations between widely-separated subsystems, which characterizes the nonlocality of magic. Our method can be implemented in a variety of situations. We describe an efficient sampling procedure using Tree Tensor Networks, that exploits their hierarchical structure leading to a modest $O(\log N)$ computational scaling with system size. To showcase the applicability and efficiency of our method, we demonstrate the importance of magic in many-body systems via the following discoveries: (a) for one dimensional systems, we show that long-range magic displays strong signatures of conformal quantum criticality (Ising, Potts, and Gaussian), overcoming the limitations of full state magic; (b) in two-dimensional $\mathbb{Z}_2$ lattice gauge theories, we provide conclusive evidence that magic is able to identify the confinement-deconfinement transition, and displays critical scaling behavior even at relatively modest volumes. Finally, we discuss an experimental implementation of the method, which only relies on measurements of Pauli observables., Comment: 18 pages, 14 figures

We consider a system of interacting spinless fermions on a two-leg triangular ladder with $\pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $\mathbb{Z}_2$ symmetry -- a product of parity transformation and chain permutation. Using bosonization, we show that, in the low-energy limit, the system is described by the quantum double-frequency sine-Gordon model. On the basis of this correspondence, a rich phase diagram of the system is obtained. It includes trivial and topological band insulators for weak interactions, separated by a Gaussian critical line, whereas at larger interactions a strongly correlated phase with spontaneously broken $\mathbb{Z}_2$ symmetry sets in, exhibiting a net charge imbalance and non-zero total current. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry. This non-Abelian symmetry, absent in the microscopic description, is realized at low-energies as a combined effect of the magnetic flux, frustration, and many-body correlations. The criticality belongs to the SU(2)$_1$ Wess-Zumino-Novikov-Witten universality class. The critical point bifurcates into two Ising critical lines that separate the band insulators from the strong-coupling symmetry broken phase. We establish an analytical connection between the low-energy description of our model around the critical bifurcation point on one hand, and the Ashkin-Teller model and a weakly dimerized XXZ spin-1/2 chain on the other. We complement our field-theory understanding via tensor network simulations, providing compelling quantitative evidences of all bosonization predictions. Our findings are of interest to up-to-date cold atom experiments utilizing Rydberg dressing, that have already demonstrated correlated ladder dynamics., Comment: 18 pages, 9 figures. Close to the published version

The presence of gauge symmetry in 1+1D is known to be redundant, since it does not imply the existence of dynamical gauge bosons. As a consequence, in the continuum, the Abelian-Higgs model, the theory of bosonic matter interacting with photons, just possesses a single phase, as the higher dimensional Higgs and Coulomb phases are connected via non-perturbative effects. However, recent research published in [Phys. Rev. Lett. 128, 090601 (2022)] has revealed an unexpected phase transition when the system is discretized on the lattice. This transition is described by a conformal field theory with a central charge of $c=3/2$. In this paper, we aim to characterize the two components of this $c=3/2$ theory -- namely the free Majorana fermionic and bosonic parts -- through equilibrium and out-of-equilibrium spectral analyses., Comment: 12 pages, 15 figures. Close to the accepted version in PRB

We investigate the nature of quantum phases arising in chiral interacting Hamiltonians recently realized in Rydberg atom arrays. We classify all possible fermionic chiral spin liquids with $\mathrm{U}(1)$ global symmetry using parton construction on the honeycomb lattice. The resulting classification includes six distinct classes of gapped quantum spin liquids: the corresponding variational wave functions obtained from two of these classes accurately describe the Rydberg many-body ground state at $1/2$ and $1/4$ particle density. Complementing this analysis with tensor network simulations, we conclude that both particle filling sectors host a spin liquid with the same topological order of a $\nu=1/2$ fractional quantum Hall effect. At density $1/2$, our results clarify the phase diagram of the model, while at density $1/4$, they provide an explicit construction of the ground state wave function with almost unit overlap with the microscopic one. These findings pave the way to the use of parton wave functions to guide the discovery of quantum spin liquids in chiral Rydberg models., Comment: 13 pages, 14 figures

We study the quantum dynamics of a many-body system subject to coherent evolution and coupled to a non-Markovian bath. We propose a technique to unravel the non-Markovian dynamics in terms of quantum jumps, a connection that was so far only understood for single-body systems. We develop a systematic method to calculate the probability of a quantum trajectory, and formulate it in a diagrammatic structure. We find that non-Markovianity renormalizes the probability of realizing a quantum trajectory, and that memory effects can be interpreted as a perturbation on top of the Markovian dynamics. We show that the diagrammatic structure is akin to that of a Dyson equation, and that the probability of the trajectories can be calculated analytically. We then apply our results to study the measurement-induced entanglement transition in random unitary circuits. We find that non-Markovianity does not significantly shift the transition, but stabilizes the volume law phase of the entanglement by shielding it from transient strong dissipation.

We consider a model of free fermions in a ladder geometry coupled to a nonuniform cavity mode via Peierls substitution. Since the cavity mode generates a magnetic field, no-go theorems on spontaneous photon condensation do not apply, and we indeed observe a phase transition to a photon condensed phase characterized by finite circulating currents, alternatively referred to as the equilibrium superradiant phase. We consider both square and triangular ladder geometries, and characterize the transition by studying the energy structure of the system, light-matter entanglement, the properties of the photon mode, and chiral currents. The transition is of first order and corresponds to a sudden change in the fermionic band structure as well as the number of its Fermi points. Thanks to the quasi-one dimensional geometry we scrutinize the accuracy of (mean field) cavity-matter decoupling against large scale density-matrix renormalization group simulations. We find that light-matter entanglement is essential for capturing corrections to matter properties at finite sizes and for the description of the correct photon state. The latter remains Gaussian in the the thermodynamic limit both in the normal and photon condensed phases., Comment: 28 pages, 9 figures. Submission to SciPost. Comments are welcome

We introduce a method for quantum simulation of U$(1)$ lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices. The proposal enables the study of both gauge and fermionic-matter fields without integrating out one of them in one and two dimensions. We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species. Starting from an $ab\,initio$ modelling of the experimental setting, we systematically carry out a derivation of the target U$(1)$ gauge theory. This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that - while pivotal for a successful implementation - have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions, and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics. We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope $^{173}$Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one- and two-dimensional settings.

We consider a model of a light-matter system, in which a system of fermions (or bosons) is coupled to a photonic mode that drives a phase transitions in the matter degrees of freedom. Starting from a simplified analytical model, we show that the entanglement between light and matter vanishes at small and large coupling strength, and shows a peak in the proximity of the transition. We perform numerical simulations for a specific model (relevant to both solid state and cold atom platforms), and show that the entanglement displays critical behavior at the transition, and features maximum susceptibility, as demonstrated by a maximal entanglement capacity. Remarkably, light-matter entanglement provides direct access to critical exponents, suggesting a novel approach to measure universal properties without direct matter probes., Comment: 10 pages; 7 figures

Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbors interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a 'spin-locked' cluster Luttinger liquid at strong interactions along each leg, as predicted by cluster bosonization. Interestingly, the competition with the zigzag interaction generates a charge density wave, a 'polarized holonic' phase, and a crystalline phase at the filling 2/5, that we address via semi-classical perturbative approach. Exact diagonalization and density matrix renormalization group simulations confirm the predictions and further characterize the phases and their transitions., Comment: Main: 6 pages, 5 figures; Supplemental Material: 11pages, 5 figures; v2: processing corrections

Recent atomic physics experiments and numerical works have reported complementary signatures of the emergence of a topological quantum spin liquid in models with blockade interactions. However, the specific mechanism stabilizing such a phase remains unclear. Here, we introduce an exact relation between an Ising-Higgs lattice gauge theory on the kagome lattice and blockaded models on Ruby lattices. This relation elucidates the origin of previously observed topological spin liquids by directly linking the latter to a deconfined phase of a solvable gauge theory. By means of exact diagonalization and unbiased quantum Monte Carlo simulations, we show that the deconfined phases extend in a broad region of the parameter space; these states are characterized by a large ground state overlap with resonating valence bond wavefunctions. These blockaded models include both creation/annihilation and hopping dynamics, and can be experimentally realized with Rydberg-dressed atoms, offering novel and controllable platforms for the engineering and characterisation of spin liquid states., Comment: 7+7 pages, 4+2 figures

We review results about entanglement (or modular) Hamiltonians of quantum many-body systems in field theory and statistical mechanics models, as well as recent applications in the context of quantum information and quantum simulation., Comment: 32 pages, 12 figures; review article

We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin-, and density-wave quasi-long-range ordering. These phases are separated by Berezinskii-Kosterlitz-Thouless, Gaussian, and supersymmetric (SUSY) quantum critical transitions. For the latter, we provide a phenomenological description of coupled SUSY conformal field theories, whose predictions are confirmed by matrix-product state simulations. Our results are motivated by, and directly relevant to, recent experiments with Rydberg-dressed atoms in optical lattices, where ladder dynamics has already been demonstrated, and emphasize the capabilities of these setups to investigate exotic quantum phenomena such as cluster liquids and coupled SUSY conformal field theories., Comment: 17 pages, 8 figures. Close to published version

In quantum statistical mechanics, finite-temperature phase transitions are typically governed by classical field theories. In this context, the role of quantum correlations is unclear: recent contributions have shown how entanglement is typically very short-ranged, and thus uninformative about long-ranged critical correlations. In this work, we show the existence of finite-temperature phase transitions where a broader form of quantum correlation than entanglement, the entropic quantum discord, can display genuine signatures of critical behavior. We consider integrable bosonic field theories in both two- and three-dimensional lattices, and show how the two-mode Gaussian discord decays algebraically with the distance even in cases where the entanglement negativity vanishes beyond nearest-neighbor separations. Systematically approaching the zero-temperature limit allows us to connect discord to entanglement, drawing a generic picture of quantum correlations and critical behavior that naturally describes the transition between entangled and discordant quantum matter., Comment: 8 pages, 7 figures

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms., Comment: accepted version, comments welcome

We study the impact of quenched disorder on the dynamics of locally constrained quantum spin chains, that describe 1D arrays of Rydberg atoms in both frozen (Ising-type) and dressed (XY-type) regime. Performing large-scale numerical experiments, we observe no trace of many-body localization even at large disorder. Analyzing the role of quenched disorder terms in constrained systems we show that they act in two, distinct and competing ways: as an on-site disorder term for the basic excitations of the system, and as an interaction between excitations. The two contributions are of the same order, and as they compete (one towards localization, the other against it), one does never enter a truly strong disorder, weak interaction limit, where many-body localization occurs. Such a mechanism is further clarified in the case of XY-type constrained models: there, a term which would represent a bona-fide local quenched disorder term acting on the excitations of the clean model must be written as a series of non-local terms in the unconstrained variables. Our observations provide a simple picture to interpret the role of quenched disorder that could be immediately extended to other constrained models or quenched gauge theories., Comment: 4 + 4 pages, comments welcome

We investigate the dynamics of two-dimensional quantum spin systems under the combined effect of random unitary gates and local projective measurements. When considering steady states, a measurement-induced transition occurs between two distinct dynamical phases, one characterized by a volume-law scaling of entanglement entropy, the other by an area-law. Employing stabilizer states and Clifford random unitary gates, we numerically investigate square lattices of linear dimension up to $L=48$ for two distinct measurement protocols. For both protocols, we observe a transition point where the dominant contribution in the entanglement entropy displays multiplicative logarithmic violations to the area-law. We obtain estimates of the correlation length critical exponent at the percent level; these estimates suggest universal behavior, and are incompatible with the universality class of 3D percolation., Comment: 10 pages + Erratum

We study the disconnected entanglement entropy, $S^D$, of the Su-Schrieffer-Heeger model. $S^D$ is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions, and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that $S^D$ behaves as a topological invariant, i.e., it is quantized to either $0$ or $2 \log (2)$ in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, $S^D$ displays a system-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of $S^D$, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants., Comment: 20 pages, 9 figures. Submission to SciPost v2: -added a section elaborating on why $S^D$ is invariant after a quench, and a section why the conclusion of the paper extend to the whole BDI class. -added references -now 25 pages, 11 figures

The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the important features of a data set - the intrinsic dimension ($I_d$) - behaves in the vicinity of phase transitions. We employ state-of-the-art nearest neighbors-based $I_d$-estimators to compute the $I_d$ of raw Monte Carlo thermal configurations across different phase transitions: first-, second-order and Berezinskii-Kosterlitz-Thouless. For all the considered cases, we find that the $I_d$ uniquely characterizes the transition regime. The finite-size analysis of the $I_d$ allows not just to identify critical points with an accuracy comparable with methods that rely on {\it a priori} identification of order parameters, but also to determine the corresponding (critical) exponent $\nu$ in case of continuous transitions. For the case of topological transitions, this analysis overcomes the reported limitations affecting other unsupervised learning methods. Our work reveals how raw data sets display unique signatures of universal behavior in the absence of any dimensional reduction scheme, and suggest direct parallelism between conventional order parameters in real space, and the intrinsic dimension in the data space.

We study the spectral properties of $D$-dimensional $N=2$ supersymmetric lattice models. We find systematic departures from the eigenstate thermalization hypothesis (ETH) in the form of a degenerate set of ETH-violating supersymmetric (SUSY) doublets, also referred to as many-body scars, that we construct analytically. These states are stable against arbitrary SUSY-preserving perturbations, including inhomogeneous couplings. For the specific case of two-leg ladders, we provide extensive numerical evidence that shows how those states are the only ones violating the ETH, and discuss their robustness to SUSY-violating perturbations. Our work suggests a generic mechanism to stabilize quantum many-body scars in lattice models in arbitrary dimensions., Comment: 9 pages, 4 figures

We carry out a comprehensive comparison between the exact modular Hamiltonian and the lattice version of the Bisognano-Wichmann (BW) one in one-dimensional critical quantum spin chains. As a warm-up, we first illustrate how the trace distance provides a more informative mean of comparison between reduced density matrices when compared to any other Schatten $n$-distance, normalized or not. In particular, as noticed in earlier works, it provides a way to bound other correlation functions in a precise manner, i.e., providing both lower and upper bounds. Additionally, we show that two close reduced density matrices, i.e. with zero trace distance for large sizes, can have very different modular Hamiltonians. This means that, in terms of describing how two states are close to each other, it is more informative to compare their reduced density matrices rather than the corresponding modular Hamiltonians. After setting this framework, we consider the ground states for infinite and periodic XX spin chain and critical Ising chain. We provide robust numerical evidence that the trace distance between the lattice BW reduced density matrix and the exact one goes to zero as $\ell^{-2}$ for large length of the interval $\ell$. This provides strong constraints on the difference between the corresponding entanglement entropies and correlation functions. Our results indicate that discretized BW reduced density matrices reproduce exact entanglement entropies and correlation functions of local operators in the limit of large subsystem sizes. Finally, we show that the BW reduced density matrices fall short of reproducing the exact behavior of the logarithmic emptiness formation probability in the ground state of the XX spin chain., Comment: 27 pages 11 Figures V2: minor changes

We show how U(1) lattice gauge theories display key signatures of ergodicity breaking in the presence of a random charge background. Contrary to the widely studied case of spin models, in the presence of Coulomb interactions, the spectral properties of such lattice gauge theories are very weakly affected by finite-volume effects. This allows to draw a sharp boundary for the ergodic regime, and thus the breakdown of quantum chaos for sufficiently strong gauge couplings, at the system sizes accessible via exact diagonalization. Our conclusions are independent on the value of a background topological angle, and are contrasted with a gauge theory with truncated Hilbert space, where instead we observe very strong finite-volume effects akin to those observed in spin chains., Comment: 7 pages, 5 figures

Variational wave functions have been a successful tool to investigate the properties of quantum spin liquids. Finding their parent Hamiltonians is of primary interest for the experimental simulation of these strongly correlated phases, and for gathering additional insights on their stability. In this work, we systematically reconstruct approximate spin-chain parent Hamiltonians for Jastrow-Gutzwiller wave functions, which share several features with quantum spin liquid wave-functions in two dimensions. Firstly, we determine the different phases encoded in the parameter space through their correlation functions and entanglement content. Secondly, we apply a recently proposed entanglement-guided method to reconstruct parent Hamiltonians to these states, which constrains the search to operators describing relativistic low-energy field theories - as expected for deconfined phases of gauge theories relevant to quantum spin liquids. The quality of the results is discussed using different quantities and comparing to exactly known parent Hamiltonians at specific points in parameter space. Our findings provide guiding principles for experimental Hamiltonian engineering of this class of states., Comment: 26 pages, 13 figures

We study the out-of-equilibrium properties of $1+1$ dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian $\mathbb{Z}_{n}$ gauge group. We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark/antiquark pairs, indicating that the system dynamics displays a number of out-of-equilibrium features., Comment: 21 pages, 17 figures

Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground state manifold, and are thus quantized to 0 or log 2. Their robust quantization property is inferred from the underlying lattice gauge theory description of topological superconductors, and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and non-trivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques., Comment: 6 pages, 8 figures. Supp Mat: 9 pages, 8 figures v2: Fused the two files into one, added a new section on disorder. Modifed the text and added relevant references. Now: 12 pages, 11 figures

We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of entanglement Hamiltonians, whose functional form is available from field theoretical insights. The method is applicable to classical simulations such as quantum Monte Carlo methods, and to experiments that allow for thermodynamic measurements such as the density of states, accessible via quantum quenches. We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law in the entanglement entropy, the number of Goldstone bosons, and to check a recent conjecture on geometric entanglement contribution at critical points described by strongly coupled field theories.

We investigate a model of hard-core bosons with infinitely repulsive nearest- and next-nearest-neighbor interactions in one dimension, introduced by Fendley, Sengupta and Sachdev in Phys. Rev. B 69, 075106 (2004). Using a combination of exact diagonalization, tensor network, and quantum Monte Carlo simulations, we show how an intermediate incommensurate phase separates a crystalline and a disordered phase. We base our analysis on a variety of diagnostics, including entanglement measures, fidelity susceptibility, correlation functions, and spectral properties. According to theoretical expectations, the disordered-to-incommensurate-phase transition point is compatible with Berezinskii-Kosterlitz-Thouless universal behaviour. The second transition is instead non-relativistic, with dynamical critical exponent $z > 1$. For the sake of comparison, we illustrate how some of the techniques applied here work at the Potts critical point present in the phase diagram of the model for finite next-nearest-neighbor repulsion. This latter application also allows to quantitatively estimate which system sizes are needed to match the conformal field theory spectra with experiments performing level spectroscopy., Comment: 18 pages, 14 figures

We introduce a method for the search of parent Hamiltonians of input wave-functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several non-trivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave-functions considerably simplifies the search for parent Hamiltonians., Comment: 5 pages, 5 figures, supplementary material

The modular (or entanglement) Hamiltonian correspondent to the half-space-bipartition of a quantum state uniquely characterizes its entanglement properties. However, in the context of lattice models, its explicit form is analytically known only for the Ising chain and certain free theories in one-dimension. In this work, we provide a throughout investigation of entanglement Hamiltonians in lattice models obtained via the Bisognano-Wichmann theorem, which provides an explicit functional form for the entanglement Hamiltonian itself in quantum field theory. Our study encompasses a variety of one- and two-dimensional models, supporting diverse quantum phases and critical points, and, most importantly, scanning several universality classes, including Ising, Potts, and Luttinger liquids. We carry out extensive numerical simulations based on the density-matrix-renormalization-group method, exact diagonalization, and quantum Monte Carlo. In particular, we compare the exact entanglement properties and correlation functions to those obtained applying the Bisognano-Wichmann theorem on the lattice. We carry out this comparison on both the eigenvalues and eigenvectors of the entanglement Hamiltonian, and expectation values of correlation functions and order parameters. Our results evidence that, as long as the low-energy description of the lattice model is well-captured by a Lorentz-invariant quantum field theory, the Bisognano-Wichmann theorem provides a qualitatively and quantitatively accurate description of the lattice entanglement Hamiltonian. The resulting framework paves the way to direct studies of entanglement properties utilizing well-established statistical mechanics methods and experiments., Comment: 19 pages, 28 figures including appendix

We investigate the ground state phase diagram of square ice -- a U(1) lattice gauge theory in two spatial dimensions -- using gauge invariant tensor network techniques. By correlation function, Wilson loop, and entanglement diagnostics, we characterize its phases and the transitions between them, finding good agreement with previous studies. We study the entanglement properties of string excitations on top of the ground state, and provide direct evidence of the fact that the latter are described by a conformal field theory. Our results pave the way to the application of tensor network methods to confining, two-dimensional lattice gauge theories, to investigate their phase diagrams and low-lying excitations., Comment: 36 pages, 16 figures; referee suggestions incorporated, added Figs. 3, 13 and appendices A, C

We discuss a one-dimensional fermionic model with a generalized $\mathbb{Z}_{N}$ even multiplet pairing extending Kitaev $\mathbb{Z}_{2}$ chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a $\mathbb{Z}_{N}$ symmetry enforcing an $N$-fold degenerate ground state robust to certain disorder. Interestingly, we show that the system supports a pair of parafermions but they are non-local instead of being boundary operators. As a result, the degeneracy of the ground state is only partly topological and coexists with spontaneous symmetry breaking by a (two-particle) pairing field. Each symmetry-breaking sector is shown to possess a pair of Majorana edge modes encoding the topological twofold degeneracy. Surrounded by two band insulators, the model exhibits for $N=4$ the dual of an $8 \pi$ fractional Josephson effect highlighting the presence of parafermions., Comment: 12 pages, 3 figures

Entanglement is central to our understanding of many-body quantum matter. In particular, the entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly correlated quantum matter from detection of topological order to characterisation of quantum critical systems. However, direct experimental measurement of the entanglement spectrum has so far remained elusive due to lack of direct experimental probes. Here we show that the entanglement spectrum of the ground state of a broad class of Hamiltonians becomes directly accessible as quantum simulation and spectroscopy of an entanglement Hamil- tonian, building on the Bisognano-Wichmann (BW) theorem of axiomatic quantum field theory. Remarkably, this theorem gives an explicit physical construction of the entanglement Hamiltonian, identified as Hamiltonian of the many-body system of interest with spatially varying couplings. Building on this, we propose an immediate, scalable recipe for implementation of the entanglement Hamiltonian, and measurement of the corresponding entanglement spectrum as spectroscopy of the Bisognano-Wichmann Hamiltonian with synthetic quantum systems, including atoms in optical lat- tices and trapped ions. We illustrate and benchmark this scenario on a variety of models, spanning phenomena as diverse as conformal field theories, topological order, and quantum phase transitions., Comment: 6 pages, 5 figures

We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, Gauss law effectively induces a dynamics which can be described as a disorder average over gauge super-selection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow entanglement growth are present in a broad regime of parameters - in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ions experiments realizing dynamical gauge fields, and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models., Comment: 5Pages + appendices; V2: updated discussion in page 2, more numerical results, added references

We show via tensor network methods that the Harper-Hofstadter Hamiltonian for hard-core bosons on a square geometry supports a topological phase realizing the $\nu=1/2$ fractional quantum Hall effect on the lattice. We address the robustness of the ground state degeneracy and of the energy gap, measure the many-body Chern number, and characterize the system using Green functions, showing that they decay algebraically at the edges of open geometries, indicating the presence of gapless edge modes. Moreover, we estimate the topological entanglement entropy by taking a combination of lattice bipartitions that reproduces the topological structure of the original proposals by Kitaev and Preskill, and Levin and Wen. The numerical results show that the topological contribution is compatible with the expected value $\gamma = 1/2$. Our results provide extensive evidence that FQH states are within reach of state-of-the-art cold atom experiments., Comment: 9 pages, 11 figures; close to published version

We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe - spin-orbit coupling and strong inter-orbital interactions - have been experimentally realized over the last two years., Comment: 12 pages (6 + 6 supplementary material)

The combination of interactions and static gauge fields plays a pivotal role in our understanding of strongly-correlated quantum matter. Cold atomic gases endowed with a synthetic dimension are emerging as an ideal platform to experimentally address this interplay in quasi-one-dimensional systems. A fundamental question is whether these setups can give access to pristine two-dimensional phenomena, such as the fractional quantum Hall effect, and how. We show that unambiguous signatures of bosonic and fermionic Laughlin-like states can be observed and characterized in synthetic ladders. We theoretically diagnose these Laughlin-like states focusing on the chiral current flowing in the ladder, on the central charge of the low-energy theory, and on the properties of the entanglement entropy. Remarkably, Laughlin-like states are separated from conventional liquids by Lifschitz-type transitions, characterized by sharp discontinuities in the current profiles, which we address using extensive simulations based on matrix-product states. Our work provides a qualitative and quantitative guideline towards the observability and understanding of strongly-correlated states of matter in synthetic ladders. In particular, we unveil how state-of-the-art experimental settings constitute an ideal starting point to progressively tackle two-dimensional strongly interacting systems from a ladder viewpoint, opening a new perspective for the observation of non-Abelian states of matter., Comment: 19 pages, 17 figures. Updated version after publication in Phys. Rev. X

We investigate the out-of-equilibrium physics of monodisperse bosonic ensembles on a square lattice. The effective Hamiltonian description of these systems is given in terms of an extended Hubbard model with cluster-forming interactions relevant to experimental realizations with cold Rydberg-dressed atoms. The ground state of the model, recently investigated in Phys. Rev. Lett. 123, 045301 (2019), features, aside from a superfluid and a stripe crystalline phase occurring at small and large interaction strength $V$, respectively, a rare first-order transition between an isotropic and an anisotropic stripe supersolid at intermediate $V$. By means of quantum Monte Carlo calculations we show that the equilibrium crystal may be turned into a glass by simulated temperature quenches and that out-of-equilibrium isotropic (super)solid states may emerge also when their equilibrium counterparts are anisotropic. These out-of-equilibrium states are of experimental interest, their excess energy with respect to the ground state being within the energy window typically accessed in cold atom experiments. We find, after quenching, no evidence of coexistence between superfluid and glassy behavior. Such an absence of superglassiness is qualitatively explained., Comment: 8 pages, 6 figures

We theoretically study a Kitaev wire interrupted by an extra site which gives rise to super exchange coupling between two Majorana bound states. We show that this system hosts a tunable, non-equlibrium Josephson effect with a characteristic $8\pi$ periodicity of the Josephson current. We elucidate the physical mechanism deriving a minimal model for the junction and confirm its quantitative accuracy by comparison to the numerical solution of the full model. The visibility of the $8\pi$ periodicity of the Josephson current is then studied using time-dependent simulations including the effects of dephasing and particle losses. Our findings provide a novel signature of Majorana quasi-particles which is qualitatively different form the behavior of a conventional superconductor, and can be experimentally verified in cold atom systems using alkaline-earth-like atoms., Comment: 6 pages, 5 figures

We propose a cold atom implementation to attain the continuum limit of (1+1)-d CP(N-1) quantum field theories. These theories share important features with (3+1)-d QCD, such as asymptotic freedom and $\theta$ vacua. Moreover, their continuum limit can be accessed via the mechanism of dimensional reduction. In our scheme, the CP(N-1) degrees of freedom emerge at low energies from a ladder system of SU(N) quantum spins, where the N spin states are embodied by the nuclear Zeeman states of alkaline-earth atoms, trapped in an optical lattice. Based on Monte Carlo results, we establish that the continuum limit can be demonstrated by an atomic quantum simulation by employing the feature of asymptotic freedom. We discuss a protocol for the adiabatic state preparation of the ground state of the system, the real-time evolution of a false $\theta$-vacuum state after a quench, and we propose experiments to unravel the phase diagram at non-zero density., Comment: Published Version, Added impurity analysis

We investigate the quantum phases of hard-core bosonic atoms in an extended Hubbard model where particles interact via soft-shoulder potentials in one dimension. Using a combination of field-theoretical methods and strong-coupling perturbation theory, we demonstrate that the low-energy phase can be a conformal cluster Luttinger liquid (CLL) phase with central charge $c=1$, where the microscopic degrees of freedom correspond to mesoscopic ensembles of particles. Using numerical density-matrix-renormalization-group methods, we demonstrate that the CLL phase, first predicted in [Phys. Rev. Lett. 111, 165302 (2013)], is separated from a conventional Tomonaga-Luttinger liquid by an exotic critical point with central charge $c=3/2$. The latter is expression of an emergent conformal supersymmetry, which is not present in the original Hamiltonian. We discuss the observability of the CLL phase in realistic experimental settings with weakly-dressed Rydberg atoms confined to optical lattices. Using quantum Monte-Carlo simulations, we show that the typical features of CLLs are stable up to comparatively high temperatures. Using exact diagonalizations and quantum trajectory methods, we provide a protocol for adiabatic state preparation as well as quantitative estimates on the effects of particle losses., Comment: 13 pages, 14 figures; updated discussion including level spectroscopy

We propose a novel platform for quantum many body simulations of dipolar spin models using current circuit QED technology. Our basic building blocks are 3D Transmon qubits where we use the naturally occurring dipolar interactions to realize interacting spin systems. This opens the way toward the realization of a broad class of tunable spin models in both two- and one-dimensional geometries. We illustrate the potential offered by these systems in the context of dimerized Majumdar-Ghosh-type phases, archetypical examples of quantum magnetism, showing how such phases are robust against disorder and decoherence, and could be observed within state-of-the-art experiments., Comment: 5 + 8 pages, 4 + 16 figures

We discuss how to locate critical points in the Berezinskii-Kosterlitz-Thouless (BKT) universality class by means of gap-scaling analyses. While accurately determining such points using gap extrapolation procedures is usually challenging and inaccurate due to the exponentially small value of the gap in the vicinity of the critical point, we show that a generic gap-scaling analysis, including the effects of logarithmic corrections, provides very accurate estimates of BKT transition points in a variety of spin and fermionic models. As a first example, we show how the scaling procedure, combined with density-matrix-renormalization-group simulations, performs extremely well in a non-integrable spin-$3/2$ XXZ model, which is known to exhibit strong finite-size effects. We then analyze the extended Hubbard model, whose BKT transition has been debated, finding results that are consistent with previous studies based on the scaling of the Luttinger-liquid parameter. Finally, we investigate an anisotropic extended Hubbard model, for which we present the first estimates of the BKT transition line based on large-scale density-matrix-renormalization-group simulations. Our work demonstrates how gap-scaling analyses can help to locate accurately and efficiently BKT critical points, without relying on model-dependent scaling assumptions., Comment: 8 pages, 7 figures

Quantum spin ice represents a paradigmatic example on how the physics of frustrated magnets is related to gauge theories. In the present work we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly admixing van der Waals interactions between laser admixed Rydberg states to the atomic ground state atoms, exploiting the strong angular dependence of interactions between Rydberg p-states together with the possibility of designing step-like potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state of the art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both s- and p-Rydberg states in exotic geometries, e.g. on a 4-8 lattice., Comment: 26 pages, 16 figures

We discuss how a lattice Schwinger model can be realized in a linear ion trap, allowing a detailed study of the physics of Abelian lattice gauge theories related to one-dimensional quantum electrodynamics. Relying on the rich quantum-simulation toolbox available in state-of-the-art trapped-ion experiments, we show how one can engineer an effectively gauge-invariant dynamics by imposing energetic constraints, provided by strong Ising-like interactions. Applying exact diagonalization to ground-state and time-dependent properties, we study the underlying microscopic model, and discuss undesired interaction terms and other imperfections. As our analysis shows, the proposed scheme allows for the observation in realistic setups of spontaneous parity- and charge-symmetry breaking, as well as false-vacuum decay. Besides an implementation aimed at larger ion chains, we also discuss a minimal setting, consisting of only four ions in a simpler experimental setup, which enables to probe basic physical phenomena related to the full many-body problem. The proposal opens a new route for analog quantum simulation of high-energy and condensed-matter models where gauge symmetries play a prominent role., Comment: 18 pages, 11 figures; v3: similar to version published in Phys. Rev. X

We investigate the effect of dipolar interactions in one-dimensional systems in connection with the possibility of observing exotic many-body effects with trapped atomic and molecular dipolar gases. By combining analytical and numerical methods, we show how the competition between short- and long-range interactions gives rise to frustrating effects which lead to the stabilization of spontaneously dimerized phases characterized by a bond-ordering. This genuine quantum order is sharply distinguished from Mott and spin-density wave phases, and can be unambiguously probed by measuring non local order parameters in-situ imaging techniques., Comment: 8 pages, 6 figures; version as published: Text added to improve readability; added extensive numerical data to support results already present in v1; section on the dipolar two-leg ladder removed for clarity; new plots and references added. Accepted for publication in Phys. Rev. A

Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic, long-range dipolar interactions play a prominent role at the many-body level. In this article we review recent theoretical studies concerning the physics of such systems. Starting from a general discussion on interaction design techniques and microscopic Hamiltonians, we provide a summary of recent work focused on many-body properties of dipolar systems, including: weakly interacting Bose gases, weakly interacting Fermi gases, multilayer systems, strongly interacting dipolar gases and dipolar gases in 1D and quasi-1D geometries. Within each of these topics, purely dipolar effects and connections with experimental realizations are emphasized., Comment: Review article; submitted 09/06/2011. 158 pages, 52 figures. This document is the unedited author's version of a Submitted Work that was subsequently accepted for publication in Chemical Reviews, copyright American Chemical Society after peer review. To access the final edited and published work, a link will be provided soon