Entanglement entropy between two coupled Tomonaga-Luttinger liquids

Abstract

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 $n\to 1$ 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, $S_n$ 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.

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)

References in corpus (21)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Bosonizing one-dimensional cold atomic gases
• Entanglement spectrum in one-dimensional systems
• Quantum Noise as an Entanglement Meter
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement Entropy in the O(N) model
• Entanglement spectra of quantum Heisenberg ladders
• Ground-state fidelity in one-dimensional gapless model
• General Relation between Entanglement and Fluctuations in One Dimension
• Unusual Corrections to Scaling in Entanglement Entropy
• Universal entanglement entropy in 2D conformal quantum critical points
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Rényi entropy of a line in two-dimensional Ising models
• Ground-state fidelity of Luttinger liquids: A wave functional approach
• Corrections to scaling for block entanglement in massive spin-chains
• Boundary contributions to specific heat and susceptibility in the spin-1/2 XXZ chain
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• The one-dimensional Hubbard model with open ends: Universal divergent contributions to the magnetic susceptibility

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