Bianchini, D. and CastroAlvaredo, O. (2016). Branch Point Twist Field Correlators in the Massive Free Boson Theory. Nuclear Physics B, 913, pp. 879911. doi: 10.1016/j.nuclphysb.2016.10.016
Abstract
Wellknown measures of entanglement in onedimensional many body quantum systems, such as the entanglement entropy and the logarithmic negativity, may be expressed in terms of the correlation functions of local fields known as branch point twist fields in a replica quantum field theory. In this “replica” approach the computation of measures of entanglement generally involves a mathematically nontrivial analytic continuation in the number of replicas. In this paper we consider twopoint functions of twist fields and their analytic continuation in the 1+1 dimensional massive (noncompactified) free Boson theory. This is one of the few theories for which all matrix elements of twist fields are known so that we may hope to compute correlation functions very precisely. We study two particular twopoint functions which are related to the logarithmic negativity of semiinfinite disjoint intervals and to the entanglement entropy of one interval. We show that our prescription for the analytic continuation yields results which are in full agreement with conformal field theory predictions in the shortdistance limit. We provide numerical estimates of universal quantities and their ratios, both in the massless (twist field structure constants) and the massive (expectation values of twist fields) theory. We find that particular ratios are given by divergent form factor expansions. We propose such divergences stem from the presence of logarithmic factors in addition to the expected powerlaw behaviour of twopoint functions at shortdistances. Surprisingly, at criticality these corrections give rise to a 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 BlondeauFournier and Doyon.
Publication Type:  Article 

Additional Information:  This is an open access article under the CC BY license(http://creativecommons.org/licenses/by/4.0/) 
Subjects:  Q Science > QC Physics 
Departments:  School of Mathematics, Computer Science & Engineering > Mathematics 
URI:  http://openaccess.city.ac.uk/id/eprint/15874 

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