Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems

TL;DR

This paper develops a quasiparticle picture for entanglement asymmetry in out-of-equilibrium quantum systems, benchmarks it in the XX spin chain, and explores how dissipation influences the quantum Mpemba effect.

Contribution

It introduces a comprehensive quasiparticle framework for charged moments in quantum quenches involving entangled multiplets, extending understanding of symmetry dynamics.

Findings

Derived a rigorous quasiparticle formula for charged moments.

Identified conditions for vanishing entanglement asymmetry at long times.

Showed dissipation can induce the quantum Mpemba effect.

Abstract

Recently, the entanglement asymmetry emerged as an informative tool to understand dynamical symmetry restoration in out-of-equilibrium quantum many-body systems after a quantum quench. For integrable systems the asymmetry can be understood in the space-time scaling limit via the quasiparticle picture, as it was pointed out in Ref. [1]. However, a quasiparticle picture for quantum quenches from generic initial states was still lacking. Here we conjecture a full-fledged quasiparticle picture for the charged moments of the reduced density matrix, which are the main ingredients to construct the asymmetry. Our formula works for quenches producing entangled multiplets of an arbitrary number of excitations. We benchmark our results in the $XX$ spin chain. First, by using an elementary approach based on the multidimensional stationary phase approximation we provide an $\textit{ab initio}$ rigorous derivation of the dynamics of the charged moments for the quench treated in [2]. Then, we show that the same results can be straightforwardly obtained within our quasiparticle picture. As a byproduct of our analysis, we obtain a general criterion ensuring a vanishing entanglement asymmetry at long times. Next, by using the Lindblad master equation, we study the effect of gain and loss dissipation on the entanglement asymmetry. Specifically, we investigate the fate of the so-called quantum Mpemba effect (QME) in the presence of dissipation. We show that dissipation can induce QME even if unitary dynamics does not show it, and we provide a quasiparticle-based interpretation of the condition for the QME.