Expectation values of twist fields and universal entanglement saturation of the free massive boson

Abstract

The evaluation of vacuum expectation values (VEVs) in massive integrable quantum field theory (QFT) is a nontrivial renormalization-group ‘connection problem’—relating large and short distance asymptotics—and is in general unsolved. This is particularly relevant in the context of entanglement entropy, where VEVs of branch-point twist fields give universal saturation predictions. We propose a new method to compute VEVs of twist fields associated to continuous symmetries in QFT. The method is based on a differential equation in the continuous symmetry parameter, and gives VEVs as infinite form-factor series which truncate at two-particle level in free QFT. We verify the method by studying twist fields in free models, which are simply related to the branch-point twist fields. We provide the first exact formulae for the VEVs of such fields in the massive uncompactified free boson model, checking against an independent calculation based on angular quantization. We show that logarithmic terms, overlooked in the original work of Callan and Wilczek (1994 Phys. Lett. B 333 55–61), appear both in the massless and in the massive situations. This implies that, in agreement with numerical form-factor observations by Bianchini and Castro-Alvaredo (2016 Nucl. Phys. B 913 879–911), the standard power-law short-distance behavior is corrected by a logarithmic factor. We discuss how this gives universal formulae for the saturation of entanglement entropy of a single interval in near-critical harmonic chains, including corrections.