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arXiv:2203.08830 · Physical review. B./Physical review. B

Weak ergodicity breaking in the Schwinger model

Jean-Yves Desaules, Debasish Banerjee, Ana Hudomal, Zlatko Papić, Arnab Sen, Jad C. Halimeh

Published May 5, 2023• 71 citations
arXivHTMLPDF

Abstract

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-$\frac{1}{2}$ quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for $S>\frac{1}{2}$ 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-$S\phantom{\rule{4pt}{0ex}}\mathrm{U}(1)$ quantum link models (QLMs) with staggered fermions. We find that QMBS persist at $S>\frac{1}{2}$, 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.

DOI
10.1103/physrevb.107.l201105

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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-12\frac{1}{2}21​ quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for S>12S>\frac{1}{2}S>21​ since such theories converge to the lattice Schwinger model in the large-SSS 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-SU(1)S\phantom{\rule{4pt}{0ex}}\mathrm{U}(1)SU(1) quantum link models (QLMs) with staggered fermions. We find that QMBS persist at S>12S>\frac{1}{2}S>21​, 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-SSS QLMs coupled to dynamical fermions, and our findings can be tested on near-term cold-atom quantum simulators of these models.
Quantum many-body scarring (QMBS) has emerged as an intriguing paradigm of weak ergodicity breaking in nonintegrable quantum many-body models, particularly lattice gauge theories (LGTs) in 1 + 1 spacetime dimensions. However, an open question is whether QMBS has a true high-energy physics origin, and thus exists in higher-dimensional LGTs with dynamical matter. Given that nonergodic dynamics in d = 1 spatial dimension tend to vanish in d > 1 , it is important to probe this question. Using matrix product state techniques for both finite and infinite systems, we show that QMBS occurs in the 2 + 1 D U ( 1 ) quantum link model, as evidenced in persistent coherent oscillations in local observables, a marked slowdown in the growth of the bipartite entanglement entropy, and revivals in the fidelity. Interestingly, we see that QMBS is more robust when the matter degrees of freedom are bosonic rather than fermionic, which we argue is due to the strong nonlocality of the wave function in the latter case. Our results further shed light on the intimate connection between gauge symmetry and QMBS, and highlight the persistence of scarring in higher spatial dimensions. Our findings can be tested in near-term analog and digital quantum simulators, and we demonstrate their accessibility on a recently proposed cold-atom analog quantum simulator.
The weak ergodicity breaking induced by quantum many-body scars (QMBSs) represents an intriguing concept that has received great attention in recent years due to its relation to unusual nonequilibrium behavior. Here, we reveal that this phenomenon can occur in a particular regime of a lattice gauge theory, where QMBSs emerge due to the presence of an extensive number of local constraints. In particular, by analyzing the gauged Kitaev model, we provide an example where QMBSs appear in a regime where charges are deconfined. By means of both numerical and analytical approaches, we find a variety of scarred states far away from the regime where the model is integrable. The presence of these states is revealed both by tracing them directly from the analytically reachable limit, as well as by quantum quenches showing persistent oscillations for specific initial states.
Quantum many-body scarring (QMBS) is an intriguing mechanism of weak ergodicity breaking that has recently spurred significant attention. Particularly prominent in Abelian lattice gauge theories (LGTs), an open question is whether QMBS nontrivially arises in non-Abelian LGTs. Here, we present evidence of robust QMBS in a non-Abelian SU ( 2 ) LGT with dynamical matter. Starting in product states that require little experimental overhead, we show that prominent QMBS arises for certain quenches, facilitated through meson and baryon-antibaryon excitations, highlighting its non-Abelian nature. The uncovered scarred dynamics manifests as long-lived coherent oscillations in experimentally accessible local observables as well as prominent revivals in the state fidelity. Our findings bring QMBS to the realm of non-Abelian LGTs, highlighting the intimate connection between scarring and gauge symmetry, and are amenable for observation in a recently proposed trapped-ion qudit quantum computer.
Recent advances in quantum simulations have opened access to the real-time dynamics of lattice gauge theories, providing a new setting to explore how quantum criticality influences thermalization and ergodicity far from equilibrium. Using QuEra's programmable Rydberg atom array, we map out the dynamical phase diagram of the spin-1/2 U(1) quantum link model in one spatial dimension by quenching the fermion mass. We reveal a tunable regime of ergodicity breaking due to quantum many-body scars, manifested as long-lived coherent oscillations that persist across a much broader range of parameters than previously observed, including at the equilibrium phase transition point. We further analyze the electron-positron pairs generated during state preparation via the Kibble-Zurek mechanism, which strongly affect the post-quench dynamics. Our results provide new insights into nonthermal dynamics in lattice gauge theories and establish Rydberg atom arrays as a powerful platform for probing the interplay between ergodicity breaking and quantum criticality.
Quantum many-body scarring (QMBS) is an intriguing mechanism of weak ergodicity breaking that has recently spurred significant attention. Particularly prominent in Abelian lattice gauge theories (LGTs), an open question is whether QMBS nontrivially arises in non-Abelian LGTs. Here, we present evidence of robust QMBS in a non-Abelian SU(2) LGT with dynamical matter. Starting in product states that require little experimental overhead, we show that prominent QMBS arises for certain quenches, facilitated through meson and baryon-antibaryon excitations, highlighting its non-Abelian nature. The uncovered scarred dynamics manifests as long-lived coherent oscillations in experimentally accessible local observables as well as prominent revivals in the state fidelity. Our findings bring QMBS to the realm of non-Abelian LGTs, highlighting the intimate connection between scarring and gauge symmetry, and are amenable for observation in a recently proposed trapped-ion qudit quantum computer.