  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.
