Symmetry-Protected Fast Relaxation and the Strong Quantum Mpemba Effect

TL;DR

This paper reveals how symmetry in open quantum systems can protect fast relaxation channels, leading to a strong quantum Mpemba effect where distant states relax faster than closer ones.

Contribution

It uncovers a symmetry-selective Liouvillian mechanism that enables symmetry-protected fast relaxation and demonstrates the resulting quantum Mpemba effect in a long-range XXZ spin chain.

Findings

Universal exponential relaxation at the SU(2) symmetric point with decay rate -2.

Breaking symmetry introduces slow modes, suppressing relaxation.

Farther states can relax faster than closer states due to symmetry filtering.

Abstract

Understanding how symmetry constrains dissipative relaxation in open quantum many-body systems remains a central challenge in nonequilibrium physics. Here we uncover a symmetry-selective Liouvillian mechanism that protects an isolated fast-decay channel in a long-range XXZ spin chain subject to dephasing noise. At the \(SU(2)\)-symmetric point, highly symmetric initial states couple exclusively to an exact Liouvillian eigenmode with decay rate \(\lambda=-2\), producing universal exponential relaxation independent of system size and interaction range. Breaking the symmetry restores overlap with slow Liouvillian modes and substantially suppresses the relaxation dynamics. This symmetry-filtered mode accessibility naturally gives rise to a strong quantum Mpemba effect, where a state farther from the steady state relaxes anomalously faster than closer thermal states. Our results establish symmetry-protected fast relaxation as a mechanism for controlling nonequilibrium pathways in open quantum systems.