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 $e^{-m/T}$ scaling in the limit $T\ll m$. We comment on the relation between our work and the Ryu-Takayanagi proposal for computing the entanglement entropy holographically.

• Received 6 November 2012

DOI:https://doi.org/10.1103/PhysRevD.87.025012