Entanglement asymmetry in the critical XXZ spin chain

We study the explicit breaking of a SU(2) symmetry to a U(1) subgroup employing the entanglement asymmetry, a recently introduced observable that measures how much symmetries are broken in a part of extended quantum systems. We consider as specific model the critical XXZ spin chain, which breaks the SU(2) symmetry of spin rotations except at the isotropic point, and is described by the massless compact boson in the continuum limit. We examine the U(1) subgroup of SU(2) that is broken outside the isotropic point by applying conformal perturbation theory, which we complement with numerical simulations on the lattice. We also analyse the entanglement asymmetry of the full SU(2) group. By relying on very generic scaling arguments, we derive an asymptotic expression for it.