Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
Florent Ferro, Filiberto Ares, Pasquale Calabrese
Abstract
Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:msub></mml:math> groups. As an application, we consider the XY spin chain, in which the ground state spontaneously breaks the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:math> 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.