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We study the entanglement entropy of the vacuum in non-relativistic localtheories with Galilean or Schr\"{o}dinger symmetry. We clear some confusion inthe literature on the free Schr\"odinger case. We find that with only positive$U(1)$ charge particles (states) and a unique zero $U(1)$ charge state (thevacuum) the entanglement entropy must vanish in that state.

Triviality of Entanglement Entropy in the Galilean Vacuum