2010/09/30 by Shunsuke Furukawa, Yong Baek Kim · 1 citation
Physics and Astronomy · #cond-mat.str-el #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevb.83.085112
published as Phys.Rev.B83:085112,2011 · 21 pages, 16 figures. v2: Some changes in the discussion of the analyticity of Renyi entropy. v3: The von Neumann limit (n\to 1) of gamma_n has been obtained. A note is added on this (Appendix C). v4: The added note has been published as Erratum: Phys. Rev. B 87, 119901(E) (2013)
arxiv created 2013/03/07 · arxiv updated 2013/03/08
We consider a system of two coupled Tomonaga-Luttinger liquids (TLL) on parallel chains and study the Renyi entanglement entropy Sn between the two chains. Here the entanglement cut is introduced between the chains, not along the perpendicular direction as used in previous studies of one-dimensional systems. The limit n→1 corresponds to the von Neumann entanglement entropy. The system is effectively described by two-component bosonic field theory with different TLL parameters in the symmetric/antisymmetric channels as far as the coupled system remains in a gapless phase. We argue that in this system, Sn is a linear function of the length of the chains (boundary law) followed by a universal subleading constant γn determined by the ratio of the two TLL parameters. The formulae of γn for integer n≥ 2 are derived using (a) ground-state wave functionals of TLLs and (b) boundary conformal field theory, which lead to the same result. These predictions are checked in a numerical diagonalization analysis of a hard-core bosonic model on a ladder. Although the analytic continuation of γn to n→ 1 turns out to be a difficult problem, our numerical result suggests that the subleading constant in the von Neumann entropy is also universal. Our results may provide useful characterization of inherently anisotropic quantum phases such as the sliding Luttinger liquid phase via qualitatively different behaviors of the entanglement entropy with the entanglement partitions along different directions.