Entanglement entropy between two coupled Tomonaga-Luttinger liquids

Understand

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.