Entanglement Entropy in Scalar Quantum Electrodynamics
Samuel Fedida, Anupam Mazumdar, Sougato Bose, Alessio Serafini
TL;DR
This work computes the vacuum entanglement entropy of a subregion in scalar QED up to two-loop order using the replica trick on conical Euclidean space, deriving Maxwell-Proca propagators in that geometry. It confirms the area law in both massive and massless limits and analyzes how loop corrections affect the RG flow of entanglement entropy, showing that entanglement decreases with energy while couplings increase, consistent with screening. The results connect entanglement entropy to renormalization-group behavior of correlations and offer a framework for extending to non-abelian theories and NLQFT, with potential insights for holography and condensed-matter analogues.
Abstract
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.