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arXiv 2301.01745hep-thcond-mat.stat-mechquant-ph
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Ising场论中复合扭场的两点函数

Two-Point Functions of Composite Twist Fields in the Ising Field Theory

Olalla A. Castro-Alvaredo, Michele Mazzoni

摘要:

在一维量子场论中,所有两体纠缠的标准度量都可以用分支点扭曲场的双折射子来表示,这里用$\mathcal{T}$和$\mathcal{T}^\dagger$来表示。这些是对称领域相关的循环置换对称的副本理论和具有最小的共形尺寸在临界点。最近,其他扭曲场(复合扭曲场),通常是更高的维度,已被证明在研究一种新的纠缠度量中发挥作用,称为对称分辨纠缠熵。本文给出了伊辛场论中复合扭转场两点函数的精确表达式。在这样做的时候,我们扩展的技术最初开发的标准分支点扭曲场的自由理论,以及现有的计算,由于霍瓦特和卡拉布雷斯的相同的两点函数,集中在领先的大距离的贡献。研究了复合扭场$\mathcal{T}_μ$及其共轭$\mathcal{T}_μ^\dagger$的基态两点函数。在临界时,该场可以被定义为$\mathcal{T}$和无序场$μ$的算子乘积展开中的主导场。我们找到了一个一般公式为$\log \langle \mathcal{T}_μ(0) \mathcal{T}^\dagger_μ(r)\rangle$和(的衍生物),其解析延续到正实副本数大于1。我们检查我们的公式的一致性表明,在短距离,它完全再现了预期的共形尺寸

英文摘要:

All standard measures of bipartite entanglement in one-dimensional quantum field theories can be expressed in terms of correlators of branch point twist fields, here denoted by $\mathcal{T}$ and $\mathcal{T}^\dagger$. These are symmetry fields associated to cyclic permutation symmetry in a replica theory and having the smallest conformal dimension at the critical point. Recently, other twist fields (composite twist fields), typically of higher dimension, have been shown to play a role in the study of a new measure of entanglement known as the symmetry resolved entanglement entropy. In this paper we give an exact expression for the two-point function of a composite twist field that arises in the Ising field theory. In doing so we extend the techniques originally developed for the standard branch point twist field in free theories as well as an existing computation due to Horváth and Calabrese of the same two-point function which focused on the leading large-distance contribution. We study the ground state two-point function of the composite twist field $\mathcal{T}_μ$ and its conjugate $\mathcal{T}_μ^\dagger$. At criticality, this field can be defined as the leading field in the operator product expansion of $\mathcal{T}$ and the disorder field $μ$. We find a general formula for $\log \langle \mathcal{T}_μ(0) \mathcal{T}^\dagger_μ(r)\rangle$ and for (the derivative of) its analytic continuation to positive real replica numbers greater than 1. We check our formula for consistency by showing that at short distances it exactly reproduces the expected conformal dimension

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