##### Ergodicity Breaking Under Confinement in Cold-Atom Quantum Simulators

J. Y. Desaules, G. X. Su, I. P. McCulloch, B. Yang, Z. Papic, J. C. Halimeh

Quantum 8, 1274 (2024).

The quantum simulation of gauge theories on synthetic quantum matter devices has gained a lot of traction in the last decade, making possible the observation of a range of exotic quantum manybody phenomena. In this work, we consider the spin -1/2 quantum link formulation of 1 + 1D quantum electrodynamics with a topological theta-angle, which can be used to tune a confinement-deconfinement transition. Exactly mapping this system onto a PXP model with mass and staggered magnetization terms, we show an intriguing interplay between confinement and the ergodicity-breaking paradigms of quantum many -body scarring and Hilbertspace fragmentation. We map out the rich dynamical phase diagram of this model, finding an ergodic phase at small values of the mass mu and confining potential x, an emergent integrable phase for large mu, and a fragmented phase for large values of both parameters. We also show that the latter hosts resonances that lead to a vast array of effective models. We propose experimental probes of our findings, which can be directly accessed in current cold -atom setups.

##### Disorder-free localization as a purely classical effect

P. Sala, G. Giudici, J. C. Halimeh

Physical Review B 109 (6), L060305 (2024).

Disorder-free localization (DFL) is an ergodicity-breaking mechanism that has been shown to occur in lattice gauge theories in the quench dynamics of initial states spanning an extensive number of gauge superselection sectors. Whether this type of DFL is intrinsically a quantum interference effect or can arise classically has hitherto remained an open question whose resolution is pertinent to further understanding the far-from-equilibrium dynamics of gauge theories. In this work, we utilize cellular automaton circuits to model the quench dynamics of large-scale quantum link model (QLM) formulations of (1 + 1)D quantum electrodynamics, showing excellent agreement with the exact quantum case for small system sizes. Our results demonstrate that DFL persists in the thermodynamic limit as a purely classical effect arising from the finite-size regularization of the gauge-field operator in the QLM formulation, and that quantum interference, though not a necessary condition, may be employed to enhance DFL.

##### Protecting Hilbert space fragmentation through quantum Zeno dynamics

P. Patil, A. Singhania, J. C. Halimeh

Physical Review B 108 (19), 195109 (2023).

Hilbert space fragmentation is an intriguing paradigm of ergodicity breaking in interacting quantum many-body systems with applications to quantum information technology, but it is usually adversely compromised in the presence of perturbations. In this work, we demonstrate the protection of constrained dynamics arising due to a combination of mirror symmetry and Hilbert space fragmentation by employing the concept of quantum Zeno dynamics. We focus on an Ising spin ladder with carefully chosen quantum fluctuations, which in the ideal case guarantee a perfect disentanglement under Hamiltonian dynamics for a large class of initial conditions. This is known to be a consequence of the interplay of Hilbert space fragmentation with a mirror symmetry, and we show numerically the effect of breaking the latter. To evince the power of this perfect disentanglement, we study the effect of generic perturbations around the fine-tuned model and show that we can protect against the undesirable growth of entanglement entropy by using a local Ising interaction on the rungs of the ladder. This allows us to suppress the entanglement entropy to an arbitrarily small value for an arbitrarily long time by controlling the strength of the rung interaction. Our work demonstrates the experimentally feasible viability of quantum Zeno dynamics in the protection of quantum information against thermalization.

##### Anatomy of dynamical quantum phase transitions

M. Van Damme, J. Y. Desaules, Z. Papic, J. C. Halimeh

Physical Review Research 5 (3), 33090 (2023).

Global quenches of quantum many-body models can give rise to periodic dynamical quantum phase transitions (DQPTs) directly connected to the zeros of a Landau order parameter (OP). The associated dynamics has been argued to bear a close resemblance to Rabi oscillations characteristic of two-level systems. Here, we address the question of whether this DQPT behavior is merely a manifestation of the limit of an effective two-level system or if it can arise as part of a more complex dynamics. We focus on quantum many-body scarring as a useful toy model allowing us to naturally study state transfer in an otherwise chaotic system. We find that a DQPT signals a change in the dominant contribution to the wave function in the degenerate initial-state manifold, with a direct relation to an OP zero only in the special case of occurring at the midpoint of an evenly degenerate manifold. Our work generalizes previous results and reveals that, in general, periodic DQPTs comprise complex many-body dynamics fundamentally beyond that of two-level systems.

##### Bridging quantum criticality via many-body scarring

A. Daniel, A. Hallam, J. Y. Desaules, A. Hudomal, G. X. Su, J. C. Halimeh, Z. Papic

Physical Review B 107 (23), 235108 (2023).

"Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals-a type of weak ergodicity breaking known as ""quantum many-body scarring"" (QMBS). Recent work [Yao, Pan, Liu, and Zhai, Phys. Rev. B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: As the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model-a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality."

##### Absence of localization in interacting spin chains with a discrete symmetry

B. Kloss, J. C. Halimeh, A. Lazarides, Y. Bar Lev

Nature Communications 14 (1), 3778 (2023).

Novel paradigms of strong ergodicity breaking have recently attracted significant attention in condensed matter physics. Understanding the exact conditions required for their emergence or breakdown not only sheds more light on thermalization and its absence in closed quantum many-body systems, but it also has potential benefits for applications in quantum information technology. A case of particular interest is many-body localization whose conditions are not yet fully settled. Here, we prove that spin chains symmetric under a combination of mirror and spin-flip symmetries and with a non-degenerate spectrum show finite spin transport at zero total magnetization and infinite temperature. We demonstrate this numerically using two prominent examples: the Stark many-body localization system (Stark-MBL) and the symmetrized many-body localization system (symmetrized-MBL). We provide evidence of delocalization at all energy densities and show that delocalization persists when the symmetry is broken. We use our results to construct two localized systems which, when coupled, delocalize each other. Our work demonstrates the dramatic effect symmetries can have on disordered systems, proves that the existence of exact resonances is not a sufficient condition for delocalization, and opens the door to generalization to higher spatial dimensions and different conservation laws. Many-body localization is an important example of non-ergodic behaviour, however the conditions for its existence and stability are not fully established. Kloss et al establish theoretically and numerically the absence of many-body localization in a broad class of spin models respecting certain symmetries.

##### Realistic scheme for quantum simulation of Z_{2} lattice gauge theories with dynamical matter in (2+1)D

L. Homeier, A. Bohrdt, S. Linsel, E. Demler, J. C. Halimeh, F. Grusdt

Communications Physics 6 (1), 127 (2023).

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.

##### Prominent quantum many-body scars in a truncated Schwinger model

J. Y. Desaules, A. Hudomal, D. Banerjee, A. Sen, Z. Papic, J. C. Halimeh

Physical Review B 107 (20), 205112 (2023).

The high level of control and precision achievable in current synthetic quantum matter setups has enabled first attempts at quantum-simulating various intriguing phenomena in condensed matter physics, including those probing thermalization or its absence in closed quantum systems. In the companion Letter to this article [J.-Y. Desaules et al., Phys. Rev. B 107, L201105 (2023)], we have shown that quantum many-body scars, special lowentropy eigenstates that weakly break ergodicity in nonintegrable systems, arise in spin-S quantum link models that converge to (1 + 1)-dimensional lattice quantum electrodynamics (Schwinger model) in the Kogut-Susskind limit S -> infinity. In this work, we further demonstrate that quantum many-body scars exist in a truncated version of the Schwinger model, and are qualitatively more prominent than their counterparts in spin-S quantum link models. We illustrate this by, among other things, performing a finite-S scaling analysis that strongly suggests that scarring persists in the truncated Schwinger model in the limit S -> infinity. Although it does not asymptotically converge to the Schwinger model, the truncated formulation is relevant to synthetic quantum matter experiments, and also provides fundamental insight into the nature of quantum many-body scars, their connection to lattice gauge theories, and the thermalization dynamics of the latter. Our conclusions can be readily tested in current cold-atom setups.

##### Weak ergodicity breaking in the Schwinger model

J. Y. Desaules, D. Banerjee, A. Hudomal, Z. Papic, A. Sen, J. C. Halimeh

Physical Review B 107 (20), L201105 (2023).

As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum many-body scars (QMBS) can offer deep insights into the thermalization dynamics of gauge theories. Having been first discovered in a spin -21 quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for S > 12 since such theories converge to the lattice Schwinger model in the large -S limit, which is the appropriate version of lattice QED in one spatial dimension. In this work, we address this question by exploring QMBS in spin -S U(1) quantum link models (QLMs) with staggered fermions. We find that QMBS persist at S > 12, with the resonant scarring regime, which occurs for a zero-mass quench, arising from simple high-energy gauge-invariant initial product states. We furthermore find evidence of detuned scarring regimes, which occur for finite-mass quenches starting in the physical vacua and the charge-proliferated state. Our results conclusively show that QMBS exist in a wide class of lattice gauge theories in one spatial dimension represented by spin -S QLMs coupled to dynamical fermions, and our findings can be tested on near-term cold-atom quantum simulators of these models.

##### Robust quantum many-body scars in lattice gauge theories

J. C. Halimeh, L. Barbiero, P. Hauke, F. Grusdt, A. Bohrdt

Quantum 7, 17 (2023).

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.

##### Dynamical quantum phase transitions in spin-S U (1) quantum link models

M. Van Damme, T. V. Zache, D. Banerjee, P. Hauke, J. C. Halimeh

Physical Review B 106 (24), 245110 (2022).

Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing far-from-equilibrium criticality in quantum many-body systems. With the strong ongoing experimental drive to quantum simulate lattice gauge theories, it becomes important to investigate DQPTs in these models in order to better understand their far-from-equilibrium properties. In this work, we use infinite matrix product state techniques to study DQPTs in spin -S U (1) quantum link models. Although we are able to reproduce literature results directly connecting DQPTs to a sign change in the dynamical order parameter in the case of S = 1/2 for quenches starting in a vacuum initial state, we find that for different quench protocols or different values of the link spin length S > 1/2 this direct connection is no longer present. In particular, we find that there is an abundance of different types of DQPTs not directly associated with any sign change of the order parameter. Our findings indicate that DQPTs are fundamentally different between the Wilson-Kogut-Susskind limit and its representation through the quantum link formalism.

##### Disorder-free localization with Stark gauge protection

H. F. Lang, P. Hauke, J. Knolle, F. Grusdt, J. C. Halimeh

Physical Review B 106 (17), 174305 (2022).

Disorder-free localization in translation-invariant gauge theories presents a counterintuitive yet powerful framework of ergodicity breaking in quantum many-body physics. The fragility of this phenomenon in the presence of gauge-breaking errors has recently been addressed, but no scheme has been able to reliably stabilize disorder-free localization through all accessible evolution times while preserving the disorder-free property. Here, we introduce the concept of Stark gauge protection, which entails a linear sum in gauge-symmetry local (pseudo)generators weighted by a Stark potential. Using exact diagonalization and Krylov-based methods, we show how this scheme can stabilize or even enhance disorder-free localization against gauge-breaking errors in U(1) and Z2 gauge theories up to all accessible evolution times, without inducing bona fide Stark many-body localization. We show through a Magnus expansion that the dynamics under Stark gauge protection is described by an effective Hamiltonian where gauge-breaking terms are suppressed locally by the protection strength and additionally by the matter site index, which we argue is the main reason behind stabilizing the localization up to all accessible times. Our scheme is readily feasible in modern ultracold-atom experiments and Rydberg-atom setups with optical tweezers.

##### Tuning the Topological theta-Angle in Cold-Atom Quantum Simulators of Gauge Theories

J. C. Halimeh, I. P. McCulloch, B. Yang, P. Hauke

Prx Quantum 3 (4), 40316 (2022).

The topological 0-angle in gauge theories engenders a series of fundamental phenomena, includ-ing violations of charge-parity (CP) symmetry, dynamical topological transitions, and confinement-deconfinement transitions. At the same time, it poses major challenges for theoretical studies, as it implies a sign problem in numerical simulations. Analog quantum simulators open the promising prospect of treat-ing quantum many-body systems with such topological terms, but, contrary to their digital counterparts, they have not yet demonstrated the capacity to control the 0-angle. Here, we demonstrate how a tunable topological 0-term can be added to a prototype theory with U(1) gauge symmetry, a discretized version of quantum electrodynamics in one spatial dimension. As we show, the model can be realized experimentally in a single-species Bose-Hubbard model in an optical superlattice with three different spatial periods, thus requiring only standard experimental resources. Through numerical calculations obtained from the time -dependent density-matrix renormalization group method and exact diagonalization, we benchmark the model system, and illustrate how salient effects due to the 0-term can be observed. These include charge confinement, the weakening of quantum many-body scarring, as well as the disappearance of Coleman's phase transition due to explicit breaking of CP symmetry. This work opens the door towards studying the rich physics of topological gauge-theory terms in large-scale cold-atom quantum simulators.

##### Driving quantum many-body scars in the PXP model

A. Hudomal, J. Y. Desaules, B. Mukherjee, G. X. Su, J. C. Halimeh, Z. Papic

Physical Review B 106 (10), 104302 (2022).

Periodic driving has been established as a powerful technique for engineering novel phases of matter and intrinsically out-of-equilibrium phenomena such as time crystals. Recent paper by Bluvstein et al. [Science 371, 1355 (2021)] has demonstrated that periodic driving can also lead to a significant enhancement of quantum many-body scarring, whereby certain nonintegrable systems can display persistent quantum revivals from special initial states. Nevertheless, the mechanisms behind driving-induced scar enhancement remain poorly understood. Here we report a detailed study of the effect of periodic driving on the PXP model describing Rydberg atoms in the presence of a strong Rydberg blockade-the canonical static model of quantum many-body scarring. We show that periodic modulation of the chemical potential gives rise to a rich phase diagram, with at least two distinct types of scarring regimes that we distinguish by examining their Floquet spectra. We formulate a toy model, based on a sequence of square pulses, that accurately captures the details of the scarred dynamics and allows for analytical treatment in the large-amplitude and high-frequency driving regimes. Finally, we point out that driving with a spatially inhomogeneous chemical potential allows to stabilize quantum revivals from arbitrary initial states in the PXP model, via a mechanism similar to prethermalization.

##### Stabilizing lattice gauge theories through simplified local pseudogenerators

J. C. Halimeh, L. Homeier, C. Schweizer, M. Aidelsburger, P. Hauke, F. Grusdt

Physical Review Research 4 (3), 33120 (2022).

The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance to be enforced for faithful quantum simulation of gauge-theory physics. This poses major experimental challenges, in large part due to the complexity of the gauge-symmetry generators. Here, we show that gauge invariance can be reliably stabilized by employing simplified local pseudogenerators designed such that within the physical sector they act identically to the actual local generator. Dynamically, they give rise to emergent exact gauge theories up to time scales polynomial and even exponential in the protection strength. This obviates the need for implementing often complex multibody full gauge symmetries, thereby further reducing experimental overhead in physical realizations. We showcase our method in the Z(2) lattice gauge theory, and discuss experimental considerations for its realization in modern ultracold-atom setups.

##### Enhancing Disorder-Free Localization through Dynamically Emergent Local Symmetries

J. C. Halimeh, L. Homeier, H. Z. Zhao, A. Bohrdt, F. Grusdt, P. Hauke, J. Knolle

Prx Quantum 3 (2), 19 (2022).

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.