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arXiv 2106.12397hep-thgr-qcquant-ph
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第一定律与全息纠缠轮廓的量子修正

First Law and Quantum Correction for Holographic Entanglement Contour

Muxin Han, Qiang Wen

备注：
v1: 23 pages, 7 figs, comments welcome; v2 22 pages, 7 figs, accepted version by Scipost Physics
发表信息：
SciPost Phys. 11 (2021) 3, 058
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摘要：

纠缠熵满足第一类定律关系，其将区域$A$的纠缠熵的一阶微扰等同于模哈密顿量$δS_{A}=δ\langle K_A \rangle$的期望值的一阶微扰。我们提出这个关系式有一个更精细的版本，即纠缠轮廓的一阶微扰等于模哈密顿量轮廓的一阶微扰，即$δs_{A}(\textbf{x})=δ\langle k_{A}(\textbf{x})\rangle$。这里，轮廓函数$s_{A}(\textbf{x})$和$k_{A}(\textbf{x})$分别捕获了$\textbf{x}$处的自由度对$S_{A}$和$K_A$的贡献。在某些简单的情况下，$k_{A}(\textbf{x})$由应力张量确定。我们还分别利用纠缠楔的精细结构和部分纠缠熵（PEE）的加性线性组合（ALC）方案计算了对纠缠轮廓的量子修正。精细结构图表明，对边界PEE的量子修正可以看作是一定体区域的体PEE。而\textit{ALC proposal}表明，对边界PEE的量子修正来自于体纠缠熵的线性组合。我们专注于全息理论与本地模块化的哈密顿量和配置的量子场论中的\textit{ALC proposal}适用。

英文摘要：

Entanglement entropy satisfies a first law-like relation, which equates the first order perturbation of the entanglement entropy for the region $A$ to the first order perturbation of the expectation value of the modular Hamiltonian, $δS_{A}=δ\langle K_A \rangle$. We propose that this relation has a finer version which states that, the first order perturbation of the entanglement contour equals to the first order perturbation of the contour of the modular Hamiltonian, i.e. $δs_{A}(\textbf{x})=δ\langle k_{A}(\textbf{x})\rangle$. Here the contour functions $s_{A}(\textbf{x})$ and $k_{A}(\textbf{x})$ capture the contribution from the degrees of freedom at $\textbf{x}$ to $S_{A}$ and $K_A$ respectively. In some simple cases $k_{A}(\textbf{x})$ is determined by the stress tensor. We also evaluate the quantum correction to the entanglement contour using the fine structure of the entanglement wedge and the additive linear combination (ALC) proposal for partial entanglement entropy (PEE) respectively. The fine structure picture shows that, the quantum correction to the boundary PEE can be identified as a bulk PEE of certain bulk region. While the \textit{ALC proposal} shows that the quantum correction to the boundary PEE comes from the linear combination of bulk entanglement entropy. We focus on holographic theories with local modular Hamiltonian and configurations of quantum field theories where the \textit{ALC proposal} applies.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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