Entanglement content of quantum particle excitations. Part I. Free field theory

Abstract

We evaluate the entanglement entropy of a single connected region in excited states of one-dimensional massive free theories with finite numbers of particles, in the limit of large volume and region length. For this purpose, we use finite-volume form factor expansions of branch-point twist field two-point functions. We find that the additive contribution to the entanglement due to the presence of particles has a simple “qubit” interpretation, and is largely independent of momenta: it only depends on the numbers of groups of particles with equal momenta. We conjecture that at large momenta, the same result holds for any volume and region lengths, including at small scales. We provide accurate numerical verifications.