  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,
non-relativistic case. Our predictions for the entanglement entropy and
correlation length are successfully compared to numerical results in two
paradigmatic systems: the Mott insulator to superfluid transition for ultracold
lattice bosons, and the ground state of ferrimagnetic systems.
