Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus

Understand

In this work, we perturbatively calculate the modular Hamiltonian to obtain the entanglement entropy in a free fermion theory on a torus with three typical deforma- tions, e.g., T\bar{T} deformation, local bilinear operator deformation, and mass deformation.

• For T\bar{T} deformation, we find that the leading order correction of entanglement entropy is proportional to the expectation value of the undeformed modular Hamiltonian.
• As a check, in the high/low-temperature limit, the entanglement entropy coincides with that obtained by the replica trick in the literature.
• Following the same perturbative strategy, we obtain the entanglement entropy of the free fermion vacuum state up to second-order by inserting a local bilinear operator deformation in a moving mirror set- ting.