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Branch point twist field correlators in the massive free Boson theory
- Source :
- Nuclear Physics B
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
Abstract
- Well-known measures of entanglement in one-dimensional 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 non-trivial analytic continuation in the number of replicas. In this paper we consider two-point functions of twist fields and their analytic continuation in the 1+1 dimensional massive (non-compactified) 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 two-point functions which are related to the logarithmic negativity of semi-infinite 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 short-distance 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 power-law behaviour of two-point functions at short-distances. 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 Blondeau-Fournier and Doyon (in preparation).<br />Comment: 35 pages, 6 figures (v3 is the published version which incorporates minor improvements)
- Subjects :
- High Energy Physics - Theory
Physics
Nuclear and High Energy Physics
Logarithm
Statistical Mechanics (cond-mat.stat-mech)
010308 nuclear & particles physics
Conformal field theory
Analytic continuation
One-dimensional space
FOS: Physical sciences
Quantum entanglement
01 natural sciences
High Energy Physics - Theory (hep-th)
Quantum mechanics
0103 physical sciences
Quantum field theory
Twist
010306 general physics
Condensed Matter - Statistical Mechanics
QC
Mathematical physics
Boson
Subjects
Details
- ISSN :
- 05503213
- Volume :
- 913
- Database :
- OpenAIRE
- Journal :
- Nuclear Physics B
- Accession number :
- edsair.doi.dedup.....d5b3743852022b85e0627b3e911a141a
- Full Text :
- https://doi.org/10.1016/j.nuclphysb.2016.10.016