Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study

TL;DR

This paper investigates the persistent breaking of $U(1)$ symmetry after a quantum quench in the XX spin chain, using entanglement asymmetry to characterize the non-restoration of symmetry over time.

Contribution

It introduces the use of entanglement asymmetry to quantify symmetry breaking after a quantum quench and provides exact descriptions of its dynamics in a non-interacting spin chain.

Findings

Symmetry remains broken at large times due to non-Abelian charges.

Entanglement asymmetry effectively characterizes symmetry breaking.

Stationary state described by a non-Abelian generalized Gibbs ensemble.

Abstract

We consider the quantum quench in the XX spin chain starting from a tilted N\'eel state which explicitly breaks the $U(1)$ symmetry of the post-quench Hamiltonian. Very surprisingly, the $U(1)$ symmetry is not restored at large time because of the activation of a non-Abelian set of charges which all break it. The breaking of the symmetry can be effectively and quantitatively characterised by the recently introduced entanglement asymmetry. By a combination of exact calculations and quasi-particle picture arguments, we are able to exactly describe the behaviour of the asymmetry at any time after the quench. Furthermore we show that the stationary behaviour is completely captured by a non-Abelian generalised Gibbs ensemble. While our computations have been performed for a non-interacting spin chain, we expect similar results to hold for the integrable interacting case as well because of the presence of non-Abelian charges also in that case.