  We carry out a numerical study of the bi-partite entanglement entropy in the
gapped regime of two paradigmatic quantum spin chain models: the Ising chain in
an external magnetic field and the anti-ferromagnetic XXZ model. The universal
scaling limit of these models is described by the massive Ising field theory
and the SU(2)-Thirring (sine-Gordon) model, respectively. We may therefore
exploit quantum field theoretical results to predict the behaviour of the
entropy. We numerically confirm that, in the scaling limit, corrections to the
saturation of the entropy at large region size are proportional to the Bessel
function K0(2mr) where m is a mass scale (the inverse correlation length) and r
the length of the region under consideration. The proportionality constant is
simply related to the number of particle types in the universal spectrum. This
was originally predicted in publications involving two of the current authors
for two-dimensional quantum field theories. Away from the universal region our
numerics suggest an entropic behaviour following quite closely the quantum
field theory prediction, except for extra dependencies on the correlation
length.
