Triviality of Entanglement Entropy in the Galilean Vacuum

TL;DR

This paper demonstrates that in non-relativistic theories with Galilean or Schrödinger symmetry, the vacuum state has zero entanglement entropy when only positive charge particles are considered, clarifying previous misconceptions.

Contribution

It clarifies the entanglement entropy behavior of the vacuum in non-relativistic theories with Galilean symmetry, resolving confusion in prior literature.

Findings

Entanglement entropy of the vacuum vanishes under specified conditions.

Clarification of previous misconceptions about entanglement in Schrödinger theories.

Analysis focused on theories with positive U(1) charge particles.

Abstract

We study the entanglement entropy of the vacuum in non-relativistic local theories with Galilean or Schr\"{o}dinger symmetry. We clear some confusion in the 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 (the vacuum) the entanglement entropy must vanish in that state.