二维扰动自由费米子Rényi熵的注记
Note on Rényi entropy of 2D perturbed free fermions
摘要：
本文研究了二维无质量自由费米子在$T\bar{T}$项和$J\bar{T}$项的一阶微扰下的Rényi熵.分析了$T\bar{T}$微扰下无限尺寸系统的真空态、$T\bar{T}$微扰下有限尺寸系统的激发态和$J\bar{T}$微扰下无限尺寸系统的真空态三种情况。我们用玻色化方法计算了Rényi熵的微扰展开式。在玻色化语言中，扭曲算符是显式已知的，利用它可以简单地计算微扰展开中的扭曲算符。此外，我们还证明了$T\bar{T}$和$J\bar{T}$项具有简单的形式，并且彼此相似。对于第一种和第三种情况，我们使用玻色化方法再现了Rényi熵的已知结果。而对于第二种情况，我们得到了新的激发态结果。
英文摘要：
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.
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