Note on Rényi entropy of 2D perturbed free fermions

Abstract

In this paper we study the Rényi 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 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 $T\bar{T}$ 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 Rényi entropy using the bosonization method. While for the second case, we obtain new results for the excited states.

22 pages

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• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Thermodynamical Property of Entanglement Entropy for Excited States
• Entanglement of low-energy excitations in Conformal Field Theory
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Cited by in corpus (4)

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• Properties of Hybrid Stars with Density Dependent Bag Model
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus