Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain

TL;DR

This paper extends the entanglement asymmetry concept to discrete cyclic groups and applies it to analyze the non-equilibrium dynamics of symmetry breaking in the XY spin chain after a quantum quench.

Contribution

It generalizes entanglement asymmetry to cyclic groups and studies its behavior in the XY spin chain's non-equilibrium dynamics.

Findings

Entanglement asymmetry can characterize symmetry breaking for cyclic groups.

The dynamics of symmetry breaking after a quantum quench are thoroughly analyzed.

Results generalize known order parameter behavior to non-equilibrium settings.

Abstract

The entanglement asymmetry is a novel quantity that, using entanglement methods, measures how much a symmetry is broken in a part of an extended quantum system. So far it has only been used to characterise the breaking of continuous Abelian symmetries. In this paper, we extend the concept to cyclic $\mathbb{Z}_N$ groups. As an application, we consider the XY spin chain, in which the ground state spontaneously breaks the $\mathbb{Z}_2$ spin parity symmetry in the ferromagnetic phase. We thoroughly investigate the non-equilibrium dynamics of this symmetry after a global quantum quench, generalising known results for the standard order parameter.