Entanglement asymmetry and quantum Mpemba effect in the XY spin chain

TL;DR

This paper investigates entanglement asymmetry in the XY spin chain, revealing a quantum Mpemba effect where greater initial symmetry breaking leads to faster restoration, with implications for understanding symmetry dynamics in quantum systems.

Contribution

It provides a comprehensive analysis of entanglement asymmetry at equilibrium and during quenches, introducing a quasi-particle picture and conditions for observing the quantum Mpemba effect in integrable systems.

Findings

Entanglement asymmetry at equilibrium relates to Cooper pairs.

Counter-intuitive faster symmetry restoration with more initial breaking.

Discontinuous dependence of symmetry restoration on criticality.

Abstract

Entanglement asymmetry is a quantity recently introduced to measure how much a symmetry is broken in a part of an extended quantum system. It has been employed to analyze the non-equilibrium dynamics of a broken symmetry after a global quantum quench with a Hamiltonian that preserves it. In this work, we carry out a comprehensive analysis of the entanglement asymmetry at equilibrium taking the ground state of the XY spin chain, which breaks the $U(1)$ particle number symmetry, and provide a physical interpretation of it in terms of superconducting Cooper pairs. We also consider quenches from this ground state to the XX spin chain, which preserves the broken $U(1)$ symmetry. In this case, the entanglement asymmetry reveals that the more the symmetry is initially broken, the faster it may be restored in a subsystem, a surprising and counter-intuitive phenomenon that is a type of a quantum Mpemba effect. We obtain a quasi-particle picture for the entanglement asymmetry in terms of Cooper pairs, from which we derive the microscopic conditions to observe the quantum Mpemba effect in this system, giving further support to the criteria recently proposed for arbitrary integrable quantum systems. In addition, we find that the power law governing symmetry restoration depends discontinuously on whether the initial state is critical or not, leading to new forms of strong and weak Mpemba effects.