Entanglement entropy in low-energy field theories at a finite chemical potential

Abstract

We investigate the leading area-law contribution to entanglement entropy in a system described by a general Lagrangian with O(2) symmetry containing first- and second-order time derivatives, namely, breaking the Lorentz invariance. We establish a connection between the Higgs gap present in a symmetry-broken phase and the area-law term for the entanglement entropy in the general nonrelativistic case. Our predictions for the entanglement entropy and correlation length are successfully compared to numerical results in two paradigmatic systems: the Mott insulator to the superfluid transition for ultracold lattice bosons and the ground state of ferrimagnetic systems.