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Entanglement entropy of non-unitary conformal field theory

Bianchini, D., Castro-Alvaredo, O., Doyon, B. , Levi, E. & Ravanini, F. (2015). Entanglement entropy of non-unitary conformal field theory. Journal of Physics A: Mathematical and Theoretical, 48(4), article number 04FT01. doi: 10.1088/1751-8113/48/4/04ft01


Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as ceff(n+1)/2n log(L), where ceff=c-24Delta > 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and Delta < 0 is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic, then there is an additional term proportional to $log(log(L)). These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.

Publication Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
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