Abstract
In this paper we study the R\'{e}nyi entropy of 2D massless free fermions perturbed by the $T\bar{T}$ term and the $J\bar{T}$ term at the first order perturbation. Three cases, the vacuum state of infinite size system with $T\bar{T}$ perturbation, the excited states of finite size system with $T\bar{T}$ perturbation, and the vacuum state of infinite size system with $J\bar{T}$ perturbation, are analyzed. We use the bosonization approach to calculate the perturbative expansions of R\'{e}nyi 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 $T\bar{T}$ and $J\bar{T}$ terms have a simple form and are similar with each other. For the first and third cases, we reproduce the known results for R\'{e}nyi entropy using the bosonization method. While for the second case, we obtain new results for the excited states.
Highlights
Quantum entanglement is a very important notion in characterizing the correlation between different subsystems in the quantum system, and it has become a topic of great interest in both high-energy physics and condensed matter physics during recent years
We mainly studied the correlator functions that appeared in the perturbation of Renyi entropy by using the bosonization approach for three cases
We considered the Renyi entropy to the first order of a vacuum state on a plane and showed that the TTterm can be written in a simple form in terms of the bosonic fields as presented in Eqs. (46) and (47)
Summary
Quantum entanglement is a very important notion in characterizing the correlation between different subsystems in the quantum system, and it has become a topic of great interest in both high-energy physics and condensed matter physics during recent years. The entanglement entropy or Renyi entropy is very difficult to calculate for the general quantum field theory (QFT). We will employ the twist operator and bosonization approaches [16,17] to study the perturbation of Renyi entropy for 2D free fermions perturbed by two particular perturbations, i.e., the TTdeformation as well as the JTdeformation. These kind of deformations in the 2D CFT have attracted much attention recently, since they have remarkable properties from the viewpoints of both field theory and holography.
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