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arXiv:2509.06642

Dissipation-Enhanced Localization in a Disorder-Free $\mathbb{Z}_2$ Lattice Gauge System

Xuanpu Yang, Xiang-Ping Jiang, Lei Pan

Published Sep 8, 2025• 0 citations
arXivHTMLPDF

Abstract

The $\mathbb{Z}_2$ lattice gauge model, as the simplest realization of a lattice gauge theory, exhibits rich and unconventional physics. One of its most remarkable features is disorder-free localization, where localization emerges not from explicit quenched disorder but from static background $\mathbb{Z}_2$ gauge charges, leading to persistent memory of the initial state. In this work, we investigate the dissipative dynamics of the $\mathbb{Z}_2$ lattice gauge model by coupling it to a Markovian environment. We find that quantum dissipation can enhance localization: memory of the initial state is retained more robustly under dissipative evolution than under unitary dynamics. This dissipation-induced enhancement of localization persists across a variety of initial states, indicating that the effect is not limited to fine-tuned configurations. Our results demonstrate that dissipation, often associated with decoherence and thermalization, can in fact serve as a powerful tool for stabilizing non-ergodic behavior in gauge-constrained quantum systems.

DOI
10.48550/arxiv.2509.06642

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Dissipation-Enhanced Localization in a Disorder-Free Z2\mathbb{Z}_2Z2​ Lattice Gauge System
The Z2\mathbb{Z}_2Z2​ lattice gauge model, as the simplest realization of a lattice gauge theory, exhibits rich and unconventional physics. One of its most remarkable features is disorder-free localization, where localization emerges not from explicit quenched disorder but from static background Z2\mathbb{Z}_2Z2​ gauge charges, leading to persistent memory of the initial state. In this work, we investigate the dissipative dynamics of the Z2\mathbb{Z}_2Z2​ lattice gauge model by coupling it to a Markovian environment. We find that quantum dissipation can enhance localization: memory of the initial state is retained more robustly under dissipative evolution than under unitary dynamics. This dissipation-induced enhancement of localization persists across a variety of initial states, indicating that the effect is not limited to fine-tuned configurations. Our results demonstrate that dissipation, often associated with decoherence and thermalization, can in fact serve as a powerful tool for stabilizing non-ergodic behavior in gauge-constrained quantum systems.
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.
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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 Z 2 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 Z 2 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 Z 2 gauge symmetry of the ideal model, associated with the Z 2 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 Z 2 pseudogenerator by providing a detailed readily implementable experimental proposal for the observation of disorder-free localization in a Rydberg setup.
Abstract Local constraint in lattice gauge theory provides an exotic mechanism inducing disorder-free localization. However, the nonequilibrium dynamics in the non-Hermition lattice gauge model has not been well understood. Here, we investigate the quench dynamics of spinless fermions with nonreciprocal hopping in the ℤ2 gauge field formed from the bond spins. Based on the effective model from duality mapping, the non-Hermitian skin effect, disorder-free localization-delocalization transition, and the real-complex transition of eigenenergies are explored systematically. By identifying the diverse scaling behaviors of quantum mutual information for fermions and spins, we predict that the non-Hermition quantum disentangled liquid presents both in localized and delocalized phase with completely different physical nature, the first comes from the ℤ2 gauge field and the second originates from the non-Hermitian skin effect. We finally show that the nonreciprocal dissipation of fermions leads the quantum information flowing from the fermions to spins. Our results provide new insights to the nonequilibrium dynamics in the gauge field, and can be experimentally verified using ultracold atoms in optical lattices.
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.
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.