Entanglement Entropy in Scalar Field Theory
  Understanding the dependence of entanglement entropy on the renormalized mass
in quantum field theories can provide insight into phenomena such as quantum
phase transitions, since the mass varies in a singular way near the transition.
Here we perturbatively calculate the entanglement entropy in interacting scalar
field theory, focussing on the dependence on the field's mass. We study lambda
phi^4 and g phi^3 theories in their ground state. By tracing over a half space,
using the replica trick and position space Green's functions on the cone, we
show that space-time volume divergences cancel and renormalization can be
consistently performed in this conical geometry. We establish finite
contributions to the entanglement entropy up to two-loop order, involving a
finite area law. The resulting entropy is simple and intuitive: the free theory
result in d=3 (that we included in an earlier publication) Delta S ~ A m^2
ln(m^2) is altered, to leading order, by replacing the bare mass m by the
renormalized mass m_r evaluated at the renormalization scale of zero momentum.
