Symmetry restoration and quantum Mpemba effect in symmetric random circuits

TL;DR

This paper explores symmetry restoration in symmetric random quantum circuits, revealing conditions under which symmetry can fail to restore and discovering a quantum Mpemba effect where more asymmetric states thermalize faster.

Contribution

It demonstrates that symmetry restoration can fail in U(1)-symmetric circuits for certain initial states and uncovers a quantum Mpemba effect in early-time dynamics of symmetry restoration.

Findings

Symmetry restoration can fail in finite-size U(1)-symmetric circuits.

A quantum Mpemba effect is observed where more asymmetric states restore symmetry faster.

The results are explained through quantum thermalization with conserved charges.

Abstract

Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and a proxy for thermalization, has recently been proposed and studied in the context of symmetry restoration for quantum many-body systems undergoing a quench. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits, particularly focusing on the U(1) symmetry case. In contrast to non-symmetric random circuits where the U(1) symmetry of a small subsystem can always be restored at late times, we reveal that symmetry restoration can fail in U(1)-symmetric circuits for certain weak symmetry-broken initial states in finite-size systems. In the early-time dynamics, we observe an intriguing quantum Mpemba effect implying that symmetry is restored faster when the initial state is more asymmetric. Furthermore, we also investigate the entanglement asymmetry dynamics for SU(2) and $Z_{2}$ symmetric circuits and identify the presence and absence of the quantum Mpemba effect for the corresponding symmetries, respectively. A unified understanding of these results is provided through the lens of quantum thermalization with conserved charges.