Note on the Rényi entropy of 2D perturbed fermions

Abstract

In this paper, we study the Rényi entropy of 2D massless free fermions perturbed by the TT̄ term and the JT̄ term. In particular, we compute the correlators in the first-order perturbation. Three cases - the vacuum state of an infinite size system with TT̄ perturbation, the excited states of a finite size system with TT̄ perturbation, and the vacuum state of an infinite size system with JT̄ perturbation - are analyzed. We use the bosonization approach to study the perturbative expansions of Rényi entropy. In the bosonization language, the twist operator is known explicitly, with which the computation of correlators in the perturbative expansion can be simply performed. Moreover, we show that the TT̄ and JT̄ terms have a simple form and are similar to each other. For the first and third cases, we reproduce the known results for Rényi entropy using the bosonization method, while for the second case, we obtain new results for the excited states.