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

• URL: http://arxiv.org/abs/2307.06902v2
• Date: Wed, 7 Feb 2024 18:12:42 GMT
• Title: Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
• Authors: Florent Ferro, Filiberto Ares, Pasquale Calabrese
• Abstract summary: 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. We consider the XY spin chain, in which the ground state spontaneously breaks the $mathbbZ$ 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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