# Entanglement entropy in low-energy field theories at finite chemical potential

## TL;DR

This paper explores how entanglement entropy behaves in non-relativistic systems with O(2) symmetry and Lorentz invariance breaking, linking the Higgs gap to entanglement properties and validating predictions with numerical results.

## Contribution

It establishes a theoretical connection between the Higgs gap and entanglement entropy in non-relativistic, symmetry-broken phases, supported by numerical comparisons.

## Key findings

- Entanglement entropy follows an area-law in the studied systems.
- The Higgs gap influences the entanglement entropy and correlation length.
- Numerical results agree with theoretical predictions in specific quantum systems.

## Abstract

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.