Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases

Understand

We study the entanglement spectrum (ES) and entropy between two coupled Tomonaga-Luttinger liquids (TLLs) on parallel periodic chains.

• This problem gives access to the entanglement properties of various interesting systems, such as spin ladders as well as two-dimensional topological phases.
• By expanding interchain interactions to quadratic order in bosonic fields, we are able to calculate the ES for both gapped and gapless systems using only methods for free theories.
• In certain gapless phases of coupled non-chiral TLLs, we interestingly find an ES with a dispersion relation proportional to the square root of the subsystem momentum, which we relate to a long-range interaction in the entanglement Hamiltonian.