Quantum Mpemba effect in Local Gauge Symmetry Restoration

TL;DR

The paper investigates whether local gauge symmetries can dynamically restore after a quench and whether the quantum Mpemba effect emerges in gauge theories. Using the (1+1)D lattice Schwinger quantum electrodynamics, it shows that the reduced-density-matrix gauge-sector structure is fixed by the initial state and that subsystem symmetry is restored in the thermodynamic limit for any finite Maxwell term J>0, while J=0 prevents restoration due to an emergent conservation law. It systematically constructs initial-state families that exhibit the QME and extends the analysis to the experimentally relevant quantum link model, proposing an order parameter for detection. These results establish the generality of the QME in locally constrained quantum systems and provide practical guidance for gauge-theory quantum simulations.

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.

Figures (6)

• Figure 1: Initial state configuration of the lattice Schwinger model. The matter field is initialized in a Néel state, consisting of alternating empty and occupied fermion sites. The gauge field on a single link within subsystem $A$ is prepared in a superposition of flux states with coefficients $\alpha_{\boldsymbol{g}_A}$, resulting in an overall initial state that is a superposition of distinct gauge sectors.
• Figure 2: The long-time equilibrium values of the EA, averaged over $wt=10^3-10^4$, as a function of the coupling strength $J$ at topological angle $\theta=\pi$ (a) and $0$ (b) for different system size $N$. (c) The distribution $|z(\omega)|$. At $\theta=\pi$, $|z(\omega)|$ remains densely distributed for all $J$, whereas at $\theta=0$, it collapses into discrete peaks equally spaced by $J$ at large couplings. The inset in (b) shows the standard deviation of a single peak increasing with the system size at fixed value of $J/w=6$.
• Figure 3: (a) and (b) show the EA dynamics for a two-site subsystem with $J=0.15$ and a three-site subsystem with $J=0.05$ in a system of size $N=16$. The insets display dynamics of initial states prepared as equal superpositions of gauge sectors, where larger $q$ leads to faster decay. By tuning the superposition coefficients, the QME is realized.
• Figure 4: Panels (a) and (b) display the quantum Mpemba effect in the quantum link model with $N=14, J/w=0.2$ and $m=0$. In panel (a), gauge-symmetry breaking is quantified using the entanglement asymmetry, while in panel (b) it is characterized by the order parameter. Both diagnostics yield the same qualitative behavior.
• Figure 5: Long-time equilibrium values of the trace distance (a–b) and the Rényi-2 entanglement asymmetry (c–d), averaged over $wt=10^3\!-\!10^4$, as a function of the coupling strength $J$ at topological angles $\theta=\pi$ and $0$ for different system sizes $N$.