Entanglement Entropy and Mutual Information in Bose-Einstein Condensates

TL;DR

This paper investigates entanglement entropy and mutual information in Bose-Einstein condensates, revealing logarithmic divergences related to particle number and condensate presence in both zero and finite temperature regimes.

Contribution

It provides the first analytical and numerical analysis of entanglement properties in non-relativistic Bose gases with Bose-Einstein condensation.

Findings

Entanglement entropy diverges logarithmically with particle number at zero temperature.

Bose-Einstein condensates cause a logarithmic divergence in mutual information at finite temperature.

The divergence's prefactor depends on the specific model studied.

Abstract

In this paper we study the entanglement properties of free {\em non-relativistic} Bose gases. At zero temperature, we calculate the bipartite block entanglement entropy of the system, and find it diverges logarithmically with the particle number in the subsystem. For finite temperatures, we study the mutual information between the two blocks. We first analytically study an infinite-range hopping model, then numerically study a set of long-range hopping models in one-deimension that exhibit Bose-Einstein condensation. In both cases we find that a Bose-Einstein condensate, if present, makes a divergent contribution to the mutual information which is proportional to the logarithm of the number of particles in the condensate in the subsystem. The prefactor of the logarithmic divergent term is model dependent.