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arXiv:2301.03006 · Physical review. B./Physical review. B

Nonthermal dynamics in a spin- 12 lattice Schwinger model

Chunping Gao, Zheng Tang, Fei Zhu, Yunbo Zhang, Han Pu, Li Chen

Published Mar 8, 2023• 7 citations
arXivHTMLPDF

Abstract

Local gauge symmetry is intriguing for the study of quantum thermalization breaking. For example, in the high-spin lattice Schwinger model (LSM), the local U(1) gauge symmetry underlies the disorder-free many-body localization (MBL) dynamics of matter fields. This mechanism, however, would not work in a spin-$\frac{1}{2}$ LSM due to the absence of electric energy in the Hamiltonian. In this paper, we show that the spin-$\frac{1}{2}$ LSM can also exhibit disorder-free MBL dynamics, as well as entropy prethermalization, by introducing a four-fermion interaction into the system. The interplay between the fermion interaction and U(1) gauge symmetry endows the gauge fields with an effectively disordered potential which is responsible for the thermalization breaking. It induces anomalous (i.e., nonthermal) behaviors in the long-time evolution of such quantities as local observables, entanglement entropy, and correlation functions. Our work offers a different platform to explore emergent nonthermal dynamics in state-of-the-art quantum simulators with gauge symmetries.

DOI
10.1103/physrevb.107.104302

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Local gauge symmetry is intriguing for the study of quantum thermalization breaking. For example, in the high-spin lattice Schwinger model (LSM), the local U(1) gauge symmetry underlies the disorder-free many-body localization (MBL) dynamics of matter fields. This mechanism, however, would not work in a spin-12\frac{1}{2}21​ LSM due to the absence of electric energy in the Hamiltonian. In this paper, we show that the spin-12\frac{1}{2}21​ LSM can also exhibit disorder-free MBL dynamics, as well as entropy prethermalization, by introducing a four-fermion interaction into the system. The interplay between the fermion interaction and U(1) gauge symmetry endows the gauge fields with an effectively disordered potential which is responsible for the thermalization breaking. It induces anomalous (i.e., nonthermal) behaviors in the long-time evolution of such quantities as local observables, entanglement entropy, and correlation functions. Our work offers a different platform to explore emergent nonthermal dynamics in state-of-the-art quantum simulators with gauge symmetries.
Localization due to the presence of disorder has proven crucial for our current understanding of relaxation in isolated quantum systems. The many-body localized phase constitutes a robust alternative to the thermalization of complex interacting systems, but recently the importance of disorder has been brought into question. A number of disorder-free localization mechanisms have been put forward connected to local symmetries of lattice gauge theories. Here, starting from translationally invariant (1+1)(1+1)(1+1)-dimensional quantum electrodynamics, we modify the dynamics of the gauge field which allows us to construct a lattice model with a UUU(1) local gauge symmetry revealing a mechanism of disorder-free localization. We consider two different discretizations of the continuum model resulting in a free-fermion soluble model in one case and an interacting model in the other. We diagnose the localization of our translationally invariant model in the far-from-equilibrium dynamics following a global quantum quench.
Many-body localization (MBL) enables new nonergodic dynamical phases of matter that avoid the fate of thermalization. Do other ergodicity-breaking phases beyond the MBL paradigm exist? Here, the authors introduce a method for constructing and probing the stability of candidate nonergodic phases. As an example, they consider disordered spin systems, in which a non-Abelian SU(2) symmetry precludes the conventional MBL phase that is characterized by quasilocal integrals of motion and area-law entanglement entropy of eigenstates. Instead, the authors construct a candidate nonergodic phase characterized by eigenstates having logarithmic scaling of entanglement entropy. They find that the phase is only marginally unstable and, therefore, nonthermal yet non-MBL dynamics can be observed in such disordered systems.
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, the Gauss law effectively induces a dynamics which can be described as a disorder average over gauge superselection 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, double-logarithmic 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 ion 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.
Disorder-free localization is a paradigm of strong ergodicity breaking that has been shown to occur in global quenches of lattice gauge theories when the system is initialized in a superposition over an extensive number of gauge sectors. Here, we show that preparing the system in a thermal Gibbs ensemble without any coherences between different gauge sectors also gives rise to disorder-free localization, with temperature acting as a disorder strength. We demonstrate our findings by calculating the quench dynamics of the imbalance of thermal ensembles in both U(1)\mathrm{U}(1)U(1) and Z2\mathbb{Z}_2Z2​ lattice gauge theories through exact diagonalization, showing greater localization with increasing ensemble temperature. Furthermore, we show how adding terms linear in local pseudogenerators can enhance temperature-induced disorder-free localization due to the dynamical emergence of an enriched local symmetry. Our work expands the realm of disorder-free localization into finite-temperature physics, and shows counterintuitively that certain quantum nonergodic phenomena can become more prominent at high temperature. We discuss the accessibility of our conclusions in current quantum simulation and computing platforms.
Lattice gauge theories, the discrete counterparts of continuum gauge theories, provide a rich framework for studying non-equilibrium quantum dynamics. Recent studies suggest disorder-free localization in the lattice Schwinger model, but its origin remains unclear. Using a combination of analytical and numerical methods, we show that Hilbert space fragmentation emerges in the strong coupling limit, constraining particle dynamics and causing sharp jumps in entanglement entropy growth within charge sectors. By analyzing jump statistics, we find that entanglement growth follows a single-logarithmic or weak power-law dependence on time, rather than a double-logarithmic form. This suggests a single ergodicity-breaking regime that mimics many-body localization in finite systems due to fragmentation effects. Our findings clarify the nature of disorder-free localization and its distinction from conventional many-body localization, highlighting how gauge constraints influence thermalization in lattice gauge theories.
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.