发表机构
Università degli Studi di Milano; University of Eastern Finland; University of Reading; University of Helsinki（米兰大学; 芬兰东部大学; 雷丁大学; 赫尔辛基大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在自由费米子链中，两个间隔一个格点的区间的互信息极限不依赖于正则化参数与块长度趋于无穷的次序，且误差有一致上界。
AI 中文摘要
在论文 J. Phys. A: Math. Theor. 53 (2020), 345303 中，计算了自由费米子链中由单个格点分隔的两个区间之间的极限互信息。该计算将熵函数替换为依赖于 $\varepsilon>0$ 的正则化版本，将块长度取至无穷，然后才让 $\varepsilon$ 趋于零。我们证明相反的次序给出相同的常数 $2\log2-1$。此外，我们表明，只要两个块长度趋于无穷且 $\varepsilon$ 同时趋于零，无论其相对速率如何，都能得到相同的极限。事实上，正则化引起的误差由 $(1+\varepsilon)\log(1+\varepsilon)-\varepsilon\log\varepsilon$ 一致地界定，且与两个块长度无关。
英文摘要
In the paper J. Phys. A: Math. Theor. 53 (2020), 345303, the limiting mutual information between two intervals separated by one lattice site in a free-fermion chain was evaluated. The calculation replaces the entropy function by a regularized version depending on $\varepsilon>0$, takes the block lengths to infinity, and only then lets $\varepsilon$ tend to zero. We prove that the opposite order gives the same constant $2\log2-1$. Moreover, we show that the same limit is obtained whenever both block lengths tend to infinity and $\varepsilon$ tends to zero simultaneously, with no restriction on their relative rates. In fact, the error caused by the regularization is bounded by $(1+\varepsilon)\log(1+\varepsilon)-\varepsilon\log\varepsilon$, uniformly in both block lengths.
