Tracing Through Scalar Entanglement

TL;DR

This paper studies the entanglement entropy of a massive scalar field at finite temperature in 1+1 dimensions, providing bounds and scaling behavior, and discusses connections to holographic entanglement entropy calculations.

Contribution

It introduces bounds on the eigenvalues of the covariance matrix and characterizes the exponential scaling of entanglement entropy in the small mass and temperature limit.

Findings

Entanglement entropy scales as exp(-m/T) for m >> T.

Bounds on the largest eigenvalues of the covariance matrix are established.

Discussion of the relation to holographic entanglement entropy via Ryu-Takayanagi proposal.

Abstract

As a toy model of a gapped system, we investigate the entanglement entropy of a massive scalar field in 1+1 dimensions at nonzero temperature. In a small mass m and temperature T limit, we put upper and lower bounds on the two largest eigenvalues of the covariance matrix used to compute the entanglement entropy. We argue that the entanglement entropy has exp(-m/T) scaling in the limit m >> T. We comment on the relation between our work and the Ryu-Takayanagi proposal for computing the entanglement entropy holographically.