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

TL;DR

This paper computes how various deformations affect entanglement entropy in a free fermion theory on a torus, using perturbative methods to analyze Tar{T}, local bilinear, and mass deformations, with consistency checks against known results.

Contribution

It provides the first perturbative calculations of entanglement entropy under multiple deformations in a free fermion system on a torus, including new insights into Tar{T} and mass deformations.

Findings

Leading order Tar{T} correction proportional to undeformed modular Hamiltonian expectation.

Entanglement entropy matches known results in high/low-temperature limits.

First and second-order corrections vanish in late-time limit for accelerated mirror.

Abstract

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. In the uniformly accelerated mirror, the first-order and second-order correction of entanglement entropy vanishes in the late time limit. For mass deformation, we derive the entanglement entropy up to first-order deformation and comment on the second-order correction.