Dynamical symmetry restoration in the Heisenberg spin chain

TL;DR

This paper investigates how the $U(1)$ symmetry is dynamically restored in the XXZ spin chain after a quench, revealing different behaviors in gapless and gapped regimes, including the quantum Mpemba effect.

Contribution

It demonstrates the role of bound states in symmetry restoration and identifies the presence or absence of the quantum Mpemba effect depending on the interaction regime.

Findings

Symmetry restoration is dominated by bound states of spinons in the gapless regime.

Slower symmetry restoration occurs as the anisotropy approaches the isotropic point.

The quantum Mpemba effect is observed in the gapless regime but absent in the gapped regime.

Abstract

The entanglement asymmetry is an observable independent tool to investigate the relaxation of quantum many body systems through the restoration of an initially broken symmetry of the dynamics. In this paper we use this to investigate the effects of interactions on quantum relaxation in a paradigmatic integrable model. Specifically, we study the dynamical restoration of the $U(1)$ symmetry corresponding to rotations about the $z$-axis in the XXZ model quenched from a tilted ferromagnetic state. We find two distinct patterns of behaviour depending upon the interaction regime of the model. In the gapless regime, at roots of unity, we find that the symmetry restoration is predominantly carried out by bound states of spinons of maximal length. The velocity of these bound states is suppressed as the anisotropy is decreased towards the isotropic point leading to slower symmetry restoration. By varying the initial tilt angle, one sees that symmetry restoration is slower for an initally smaller tilt angle, signifying the presence of the quantum Mpemba effect. In the gapped regime however, spin transport for non maximally tilted states, is dominated by smaller bound states with longer bound states becoming frozen. This leads to a much longer time scales for restoration compared to the gapless regime. In addition, the quantum Mpemba effect is absent in the gapped regime.