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Well-known measures of entanglement in one-dimensional many body quantumsystems, such as the entanglement entropy and the logarithmic negativity, maybe expressed in terms of the correlation functions of local fields known asbranch point twist fields in a replica quantum field theory. In this "replica"approach the computation of measures of entanglement generally involves amathematically non-trivial analytic continuation in the number of replicas. Inthis paper we consider two-point functions of twist fields and their analyticcontinuation in the 1+1 dimensional massive (non-compactified) free Bosontheory. This is one of the few theories for which all matrix elements of twistfields are known so that we may hope to compute correlation functions veryprecisely. We study two particular two-point functions which are related to thelogarithmic negativity of semi-infinite disjoint intervals and to theentanglement entropy of one interval. We show that our prescription for theanalytic continuation yields results which are in full agreement with conformalfield theory predictions in the short-distance limit. We provide numericalestimates of universal quantities and their ratios, both in the massless (twistfield structure constants) and the massive (expectation values of twist fields)theory. We find that particular ratios are given by divergent form factorexpansions. We propose such divergences stem from the presence of logarithmicfactors in addition to the expected power-law behaviour of two-point functionsat short-distances. Surprisingly, at criticality these corrections give rise toa log(logL) correction to the entanglement entropy of one interval of length L.This hitherto overlooked result is in agreement with results by Calabrese,Cardy and Tonni and has been independently derived by Blondeau-Fournier andDoyon (in preparation).

Branch Point Twist Field Correlators in the Massive Free Boson Theory