Measurement-induced symmetry restoration and quantum Mpemba effect

TL;DR

This paper shows that measurements in quantum many-body systems can induce symmetry restoration and cause a quantum Mpemba effect, where more asymmetric states relax faster to symmetry under certain measurement conditions.

Contribution

It reveals a measurement-induced symmetry restoration mechanism and demonstrates the quantum Mpemba effect driven by non-Hermitian dynamics in monitored quantum systems.

Findings

Measurement induces symmetry restoration above a critical rate.

Systems exhibit a quantum Mpemba effect with faster relaxation of more asymmetric states.

Symmetry remains broken below the measurement threshold.

Abstract

Monitoring a quantum system can profoundly alter its dynamical properties, leading to nontrivial emergent phenomena. In this work, we demonstrate that dynamical measurements strongly influence the evolution of symmetry in many-body quantum systems. Specifically, we demonstrate that monitored systems governed by non-Hermitian dynamics exhibit a quantum Mpemba effect, where systems with stronger initial asymmetry relax faster to a symmetric state. Crucially, this phenomenon is purely measurement-induced: in the absence of measurements, we find states where the corresponding unitary evolution does not display any Mpemba effect. Furthermore, we uncover a novel measurement-induced symmetry restoration mechanism: below a critical measurement rate, the symmetry remains broken, but beyond a threshold, it is fully restored in the thermodynamic limit--along with the emergence of the quantum Mpemba effect.