2014/05/31 by Davide Bianchini, Olalla A. Castro-Alvaredo, Benjamin Doyon +2 · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/1751-8113/48/4/04ft01
5 pages, 2 figures. Revised version including new derivation of the EE of logarithmic CFT. To appear in J. Phys. A. (fast track communications)
arxiv created 2014/12/22 · arxiv updated 2015/06/19
In this letter 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 Sn ∼ \fracceff(n+1)6n log ℓ, where ceff=c-24Δ>0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and Δ≠ 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 (L0 = ΔI + N with N nilpotent), 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.