  We find the entanglement entropy of a subregion of the vacuum state in scalar
quantum electrodynamics, working perturbatively to the 2-loops level. Doing so
leads us to derive the Maxwell-Proca propagator in conical Euclidean space. The
area law of entanglement entropy is recovered in both the massive and massless
limits of the theory, as is expected. These results yield the renormalisation
group flow of entanglement entropy, and we find that loop contributions
suppress entanglement entropy. We highlight these results in the light of the
renormalization group flow of couplings and correlators, which are increased in
scalar quantum electrodynamics, so that the potential tension between the
increase in correlations between two points of spacetime and the decrease in
entanglement entropy between two regions of spacetime with energy is discussed.
We indeed show that the vacuum of a subregion of spacetime purifies with energy
in scalar quantum electrodynamics, which is related to the concept of
screening.
