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.

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• Entanglement entropies of an interval in the free Schrödinger field theory at finite density