Multiple crossing during dynamical symmetry restoration and implications for the quantum Mpemba effect

TL;DR

This paper explores how the symmetry restoration dynamics in quantum many-body systems can exhibit multiple crossings, revealing complex behaviour beyond the previously observed single crossing Mpemba effect.

Contribution

It demonstrates that, by tuning initial states in free fermionic systems, the entanglement asymmetry can show multiple crossings, indicating richer symmetry dynamics than previously known.

Findings

Multiple crossings of entanglement asymmetry observed

Rich symmetry dynamics in free fermionic models

Implications for quantum Mpemba effect understanding

Abstract

Local relaxation after a quench in 1-D quantum many-body systems is a well known and very active problem with rich phenomenology. Except for pathological cases, the local relaxation is accompanied by the local restoration of the symmetries broken by the initial state that are preserved by the unitary evolution. Recently, the entanglement asymmetry has been introduced as a probe to study the interplay between symmetry breaking and relaxation in an extended quantum system. In particular, using the asymmetry, it has been shown that the more a symmetry is initially broken, the faster it may be restored. This surprising effect, which has been also observed in trapped-ion experiments, can be seen as a quantum version of the Mpemba effect and is manifested by the crossing at a finite time of the entanglement asymmetry curves of two different initial symmetry breaking configurations. In this paper we show, how, by tuning the initial state, the symmetry dynamics in free fermionic systems can display much richer behaviour than seen previously. In particular, for certain classes of initial states, including ground states of free fermionic models with long-range couplings, the entanglement asymmetry can exhibit multiple crossings. This illustrates that the existence of the quantum Mpemba effect can only be inferred by examining the late time behaviour of the entanglement asymmetry.