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arXiv:1706.05878 · Physical Review Letters

Many-Body Localization Dynamics from Gauge Invariance

Marlon Brenes, Marcello Dalmonte, Markus Heyl, Antonello Scardicchio

Published Jan 19, 2018• 180 citations
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Abstract

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.

DOI
10.1103/physrevlett.120.030601

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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.
Quantum-state complexity diagnostics provide valuable insight into many-body dynamics, information scrambling, and quantum computation. Here, we investigate the real-time dynamics of quantum complexity in 1+11+11+1-dimensional Abelian U(1) and non-Abelian SU(2) lattice gauge theories (LGTs), focusing on the disorder-free localization (DFL) regime. Using stabilizer Rényi entropy, participation Rényi entropy, and fermionic non-Gaussianity as measures of complexity, we observe, for both theories, two main behaviors as a function of the gauge coupling: at intermediate values, a power-law relaxation towards saturation, consistent with observations in many-body localization, and, at sufficiently large values, an ultraslow double-logarithmic growth, which we substantiate with a configuration-space bound verified by exact counting. Our results not only provide deeper insight into the dynamics of DFL but also highlight the role of gauge invariance in constraining quantum resources and are relevant to recent quantum simulations of LGTs.
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.
We study quantum quenches in two-dimensional lattice gauge theories with fermions coupled to dynamical Z2{\mathbb{Z}}_{2}Z2​ gauge fields. Through the identification of an extensive set of conserved quantities, we propose a generic mechanism of charge localization in the absence of quenched disorder both in the Hamiltonian and in the initial states. We provide diagnostics of this localization through a set of experimentally relevant dynamical measures, entanglement measures, as well as spectral properties of the model. One of the defining features of the models that we study is a binary nature of emergent disorder, related to Z2{\mathbb{Z}}_{2}Z2​ degrees of freedom. This results in a qualitatively different behavior in the strong disorder limit compared to typically studied models of localization. For example, it gives rise to a possibility of a delocalization transition via a mechanism of quantum percolation in dimensions higher than 1D. We highlight the importance of our general phenomenology to questions related to dynamics of defects in Kitaev's toric code, and to quantum quenches in Hubbard models. While the simplest models we consider are effectively noninteracting, we also include interactions leading to many-body localizationlike logarithmic entanglement growth. Finally, we consider effects of interactions that generate dynamics for conserved charges, which gives rise to only transient localization behavior, or quasi-many-body localization.
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.
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.
Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication [Nature 534, 516 (2016)], we proposed and experimentally demonstrated a digital quantum simulation of the paradigmatic Schwinger model, a U(1)-Wilson lattice gauge theory describing the interplay between fermionic matter and gauge bosons. Here, we provide a detailed theoretical analysis of the performance and the potential of this protocol. Our strategy is based on analytically integrating out the gauge bosons, which preserves exact gauge invariance but results in complicated long-range interactions between the matter fields. Trapped-ion platforms are naturally suited to implementing these interactions, allowing for an efficient quantum simulation of the model, with a number of gate operations that scales only polynomially with system size. Employing numerical simulations, we illustrate that relevant phenomena can be observed in larger experimental systems, using as an example the production of particle--antiparticle pairs after a quantum quench. We investigate theoretically the robustness of the scheme towards generic error sources, and show that near-future experiments can reach regimes where finite-size effects are insignificant. We also discuss the challenges in quantum simulating the continuum limit of the theory. Using our scheme, fundamental phenomena of lattice gauge theories can be probed using a broad set of experimentally accessible observables, including the entanglement entropy and the vacuum persistence amplitude.