  In the face of mounting numerical evidence, Metlitski and Grover
[arXiv:1112.5166] have given compelling analytical arguments that systems with
spontaneous broken continuous symmetry contain a sub-leading contribution to
the entanglement entropy that diverges logarithmically with system size. They
predict that the coefficient of this log is a universal quantity that depends
on the number of Goldstone modes. In this paper, we confirm the presence of
this log term through quantum Monte Carlo calculations of the second R\'enyi
entropy on the spin 1/2 XY model. Devising an algorithm to facilitate
convergence of entropy data at extremely low temperatures, we demonstrate that
the single Goldstone mode in the ground state can be identified through the
coefficient of the log term. Furthermore, our simulation accuracy allows us to
obtain an additional geometric constant additive to the R\'enyi entropy, that
matches a predicted fully-universal form obtained from a free bosonic field
theory with no adjustable parameters.
