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

Abstract

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 U(1) 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 & Wilczek [Phys. Lett. B333 (1994)], appear both in the massless and in the massive situations. This implies that, in agreement with numerical form-factor observations by Bianchini & Castro-Alvaredo [Nucl. Phys. B913 (2016)], 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 log log corrections.

Spectral determinants for twist field correlators

“…[43] and via analytical methods in Ref. [44], though our sign is opposite to the one in the first study.…”

Entanglement content of quantum particle excitations. Part II. Disconnected regions and logarithmic negativity

“…The form factors of the U p1q twist fields will constitute the building blocks of all our computations so we will recall the main formulae here. They can be computed by the standard techniques [50,51,52] and have been known for a long time [53,54]. The formulae that we will need here are:…”

Quantum integrability and quantum groups: a special issue in memory of Petr P Kulish

“…A certain topological CFT is explicitly analyzed in [12]. A new method of computation of vacuum expectation values (VEV) in massive integrable field theories is proposed in [13], it leads, in particular, to some new predictions for the quantum entanglement entropy. Macdonald refined topological vertex introduced and studied in [14] is a combinatorial construction closely related to the instanton partition function and AGT conjecture Several contributions explore integrability in planar AdS/CFT.…”