Quantum Mpemba effect in Local Gauge Symmetry Restoration

TL;DR

This paper investigates the quantum Mpemba effect in gauge theories, demonstrating that gauge symmetry can be dynamically restored in certain conditions, with implications for quantum simulations of gauge systems.

Contribution

It reveals the occurrence of the quantum Mpemba effect in local gauge symmetries and constructs initial states exhibiting this phenomenon, supported by analytical and numerical evidence.

Findings

Gauge symmetry restoration depends on the Maxwell term presence.

Subsystem gauge symmetry is restored in the thermodynamic limit with finite Maxwell term.

The quantum Mpemba effect is demonstrated in gauge theories and linked to experimental realizations.

Abstract

Understanding relaxation in isolated quantum many-body systems remains a central challenge. Recently, the quantum Mpemba effect (QME), a counterintuitive relaxation phenomenon, has attracted considerable attention and has been extensively studied in systems with global symmetries. Here, we study the QME in gauge theories with massive local gauge symmetries. In the lattice Schwinger model, we demonstrate that the gauge structure of the reduced density matrix of a subsystem is entirely determined by the initial state and remain unchanged during the time evolution. We then investigate whether gauge symmetry can be dynamically restored following a symmetric quench. Analytical and numerical results show that when the Maxwell term is zero, gauge symmetry restoration fails due to the emergence of a peculiar conservation law. However, for any finite Maxwell term, subsystem gauge symmetry is restored in the thermodynamic limit. Based on these results, we systematically construct a families of initial states exhibiting the QME. We further explore the QME in the quantum link model-a truncated lattice Schwinger model, which has been realized in experiments. Moreover, we propose an experimentally accessible order parameter that correctly captures the QME. Our work demonstrates the generality of the quantum Mpemba effect even in the local gauge symmetries, and are directly relevant to ongoing quantum simulation experiments of gauge theories.