Sara Murciano
The interplay between entanglement and symmetries has attracted lot of attention in the last years. In the presence of a conserved charge, the reduced density matrix admits a block diagonal decomposition in the eigenbasis of the conserved charge and we can define the notion of the entanglement in a given block (the symmetry resolved entanglement). Despite this nice structure is destroyed when the symmetry is broken, one can wonder whether entanglement can still 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. I will show two neat setups of a quantum quench of a spin chain with an initially broken global U(1) symmetry, emphasising how the asymmetry is able to capture whether the symmetry is restored dynamically or not. In the former case, one can observe the counterintuitive result that the more the symmetry is initially broken, the faster it is restored, a sort of quantum Mpemba effect.