A probe of symmetry breaking from entanglement

Symmetries and entanglement are two of the pillars of modern quantum physics. Recently there has been a huge research activity on the interplay between these two notions. So far, it has been focused on studying entanglement in the charge sectors of a system with internal symmetries. Still, one can wonder whether entanglement can be used also to quantify how much a symmetry is broken in a system, an issue that has received little attention until now.

Hence, using methods from the theory of entanglement in many-body quantum systems, I present a subsystem measure of symmetry breaking, that we call entanglement asymmetry. As a prototypical illustration, I study the entanglement asymmetry in a quantum quench of a spin chain in which an initially broken global U(1) symmetry is restored dynamically. I will show that, expectedly, the larger is the subsystem, the slower is the restoration, but also the counterintuitive result that the more the symmetry is initially broken, the faster it is restored, a sort of quantum Mpemba effect.