论文标题
从Renyi熵中提取von Neumann熵的另一种方法
An Alternative Method for Extracting the von Neumann Entropy from Renyi Entropies
论文作者
论文摘要
提出了一种替代方法，用于从$ \ operatatorName {tr} $中提取von neumann熵$ - \ operatotorName {tr}（ρ\lnρ）$，用于量子系统中的量子系统中的整数$ n $的$ \ operatatorName {tr}（ρ^n）$。该方法不依赖于$ n $中的直接分析延续，而是使用生成函数$ - \ operatotorName {tr} \ {ρ\ ln [（1-zρ） /（1-zρ） /（1-z） /（1-z）] \} $的$ z $。生成功能的泰勒系列绝对是$ | z | <1 $的绝对收敛性，并且可以在$ z $中进行分析继续，至$ z = - \ infty $，它给出了von Neumann熵。例如，我们使用该方法在分析中以较小的交叉比例极限分析了两个间隔的CFT纠缠熵，从而再现了Calabrese等人的结果。由Direct Analytic Continuation以$ n $ $ N $获得。通过数值计算的数值计算，用于对纠缠的一般交叉比和有限温度和有限间隔长度的一个间隔的纠缠熵计算。
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.
