A simpler probe of the quantum Mpemba effect in closed systems

TL;DR

This paper introduces a simple, computationally efficient method to probe the relaxation dynamics of closed quantum systems, re-examines the quantum Mpemba effect, and identifies conditions under which it occurs or is suppressed.

Contribution

It presents an entropy difference approximation for relative entropy, relates it to entanglement asymmetry, and provides criteria for the quantum Mpemba effect in various models.

Findings

The entropy difference effectively approximates relative entropy during relaxation.

The quantum Mpemba effect occurs under specific symmetry and quasiparticle conditions.

In entanglement membrane models, the effect is generally suppressed.

Abstract

We study the local relaxation of closed quantum systems through the relative entropy between the reduced density matrix and its long time limit. We show, using analytic arguments combined with numerical checks, that this relative entropy can be very well approximated by an entropy difference, affording a significant computational advantage. We go on to relate this to the entanglement asymmetry of the subsystem with respect to time translation invariance. In doing this, we obtain a simple probe of the relaxation dynamics of closed many-body systems and use it to re-examine the quantum Mpemba effect, wherein states can relax faster if they are initially further from equilibrium. We reproduce earlier instances of the effect related to symmetry restoration as well as uncover new cases in the absence of such symmetries. For integrable models, we obtain the criteria for this to occur using the quasiparticle picture. Lastly, we show that, in models obeying the entanglement membrane picture, the quantum Mpemba effect cannot occur for a large class of initial states.