Triviality of entanglement entropy in the Galilean vacuum

Abstract

We study the entanglement entropy of the vacuum in non-relativistic local theories with Galilean or Schrödinger symmetry. We clear some confusion in the literature on the free Schrödinger case. We find that with only positive U(1) charge particles (states) and a unique zero U(1) charge state (the vacuum) the entanglement entropy must vanish in that state.