Entanglement and Symmetry Breaking

This thesis studies (generalized) symmetry breaking in states via entanglement measures. Specifically, we study a relative entropy between a given state and a suitably defined symmetric version of the same state; obtained by applying a quantum channel made of the topological operators implementing the symmetry. We study this for both excited states in CFTs as well as symmetry breaking vacua. In the first part, following [1], we study a perturbative version of this asymmetry in CFTs for a U(1) symmetry in various geometries, and study the relaxation of such states in real time while displaying a quantum Mpemba effect. We also study the holography of entanglement asymmetry. In the second part, following [2], we study the symmetrization process for non-invertible symmetries in two spacetime dimensions. We identify the different symmetry algebras that act on a circle or interval hilbert space, and prescribe a universal, unique symmetrization procedure to compute symmetry breaking. We study examples in both CFTs and gapped symmetry breaking states.