Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-09-15
Phys.Rev.B83:085112,2011
Physics
Condensed Matter
Strongly Correlated Electrons
19 pages, 14 figures. v2: Some changes in the discussion of the analyticity of Renyi entropy
Scientific paper
10.1103/PhysRevB.83.085112
We consider a system of two coupled Tomonaga-Luttinger liquids (TLL) on parallel chains and study the Renyi entanglement entropy $S_n$ 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 $n\to1$ 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, $S_n$ is a linear function of the length of the chains (boundary law) followed by a universal subleading constant $\gamma_n$ determined by the ratio of the two TLL parameters. The formulae of $\gamma_n$ for integer $n\ge 2$ 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 $\gamma_n$ to $n\to 1$ 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.
Furukawa Shunsuke
Kim Yong Baek
No associations
LandOfFree
Entanglement entropy between two coupled Tomonaga-Luttinger liquids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Entanglement entropy between two coupled Tomonaga-Luttinger liquids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entanglement entropy between two coupled Tomonaga-Luttinger liquids will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-26684