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arXiv:2302.00681 · Physical review. B./Physical review. B

Disorder-free localization as a purely classical effect

Pablo Sala, Giuliano Giudici, Jad C. Halimeh

Published Feb 28, 2024• 5 citations
arXivHTMLPDF

Abstract

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 $(1+1)\mathrm{D}$ 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.

DOI
10.1103/physrevb.109.l060305

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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(1+1)\mathrm{D}(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.
Disorder-Free Localization in 2+12+12+1D Lattice Gauge Theories with Dynamical Matter
Disorder-free localization (DFL) has been established as a mechanism of strong ergodicity breaking in 1+11+11+1D lattice gauge theories (LGTs) with dynamical matter for quenches starting in homogeneous initial states that span an extensive number of gauge superselection sectors. Nevertheless, the fate of DFL in 2+12+12+1D in the presence of dynamical matter has hitherto remained an open question of great interest in light of the instability of quenched-disorder many-body localization in higher spatial dimensions. Using infinite matrix product state calculations, we show that DFL survives in 2+12+12+1D LGTs, albeit it is generally less pronounced than in 1+11+11+1D, and highly depends on the matter configuration of the initial state. Through suitable matter configurations, we are able to relate and compare the 1+11+11+1D and 2+12+12+1D cases, showing that the main ingredient for the strength of DFL in our setup is the \textit{propagation directionality} of matter. Our results suggest that, generically, DFL is weakened with increasing spatial dimension, although it can be made independent of the latter by minimizing the propagation directionality of matter in the initial state.
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.
Disorder-free localization has been proposed as a mechanism for ergodicity breaking in lattice gauge theories (LGTs) which can even occur in two spatial dimensions (2D). It has been shown that the U(1) quantum link model (QLM) can localize due to an emergent classical percolation transition fragmenting the system into disconnected real-space clusters. While the nature of the quantum localization transition (QLT) is still debated for conventional many-body localization, here we provide a comprehensive characterization of the QLT for the QLM in 2D for a disorder-free case. In this Letter we find compelling evidence that the QLT in the 2D QLM is continuous and we determine its universality class. We base our considerations on a spectral analysis of finite-size clusters in the percolation problem which exhibits two regimes---one in which large clusters effectively behave nonergodically, a result naturally accounted for as an interference phenomenon in configuration space, and the other in which all large clusters behave ergodically. Our analysis can also be applied to other 2D U(1) LGTs potentially including also matter degrees of freedom.
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.
Disorder-free localization is a paradigm of nonergodicity in translation-invariant quantum many-body systems hosting gauge symmetries. The quench dynamics starting from simple initial states, which correspond to extensive superpositions of gauge superselection sectors, exhibits many-body localization with the system dynamically inducing its own disorder. An open question concerns the stability of disorder-free localization in the presence of gauge-breaking errors, and whether processes due to the latter can be controllably suppressed. Here, we show that translation-invariant \textit{single-body gauge terms} induce a quantum Zeno effect that reliably protects disorder-free localization against errors up to times at least polynomial in the protection strength. Our experimentally feasible scheme not only shows that disorder-free localization can be reliably stabilized, but also opens promising prospects for its observation in quantum simulators.
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.