arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2008.10076hep-th
收藏

从Renyi熵提取冯诺伊曼熵的一种新方法

An Alternative Method for Extracting the von Neumann Entropy from Renyi Entropies

Eric D'Hoker, Xi Dong, Chih-Hung Wu

备注：
24 pages, 4 figures
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

提出了一种从密度矩阵为$ρ$的量子系统中的整数$n$的$\operatorname{Tr} (ρ^n)$中提取冯诺伊曼熵$-\operatorname{Tr} (ρ\ln ρ)$的方法。该方法不依赖于$n$中的直接解析延拓，而是使用辅助复变量$z$的生成函数$-\operatorname{Tr} \{ ρ\ln [(1-z ρ) / (1-z)] \}$。生成函数具有在$|z|<1$内绝对收敛的泰勒级数，并且可以在$z$中解析地继续到$z = -\infty$，其中它给出冯诺伊曼熵。作为例子，我们用该方法解析计算了小交比极限下两个区间的CFT纠缠熵，再现了Calabrese等人在$n$中直接解析延拓得到的结果.进一步的例子提供了数值计算的纠缠熵的两个区间的一般交比，和一个区间在有限的温度和有限的区间长度。

英文摘要：

An alternative method is presented for extracting the von Neumann entropy $-\operatorname{Tr} (ρ\ln ρ)$ from $\operatorname{Tr} (ρ^n)$ for integer $n$ in a quantum system with density matrix $ρ$. Instead of relying on direct analytic continuation in $n$, the method uses a generating function $-\operatorname{Tr} \{ ρ\ln [(1-z ρ) / (1-z)] \}$ of an auxiliary complex variable $z$. The generating function has a Taylor series that is absolutely convergent within $|z|<1$, and may be analytically continued in $z$ to $z = -\infty$ where it gives the von Neumann entropy. As an example, we use the method to calculate analytically the CFT entanglement entropy of two intervals in the small cross ratio limit, reproducing a result that Calabrese et al. obtained by direct analytic continuation in $n$. Further examples are provided by numerical calculations of the entanglement entropy of two intervals for general cross ratios, and of one interval at finite temperature and finite interval length.

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。

↑