非齐次XX自旋链和拟精确可解模型
Inhomogeneous XX spin chains and quasi-exactly solvable models
摘要：
我们建立了一个直接连接之间的非均匀XX自旋链（或自由费米子系统与最近邻跳跃）和某些QES模型的线上产生一个家庭的弱正交多项式。我们对所有这些模型及其相关的XX链进行了分类，其中包括与线上的Lamé（有限能隙）量子势相关的两个家族。对于这些链之一，我们数值计算的雷尼二分纠缠熵在半填充，并推导出一个渐近近似的研究模型的连续极限，它原来描述了一个无质量的狄拉克费米子在一个适当的弯曲的背景。我们表明，领先的熵的行为是一个$c=1$临界系统，虽然有一个subleading $\log(\log N)$校正（其中$N$是网站的数量）不寻常的这种类型的模型。
英文摘要：
We establish a direct connection between inhomogeneous XX spin chains (or free fermion systems with nearest-neighbors hopping) and certain QES models on the line giving rise to a family of weakly orthogonal polynomials. We classify all such models and their associated XX chains, which include two families related to the Lamé (finite gap) quantum potential on the line. For one of these chains, we numerically compute the Rényi bipartite entanglement entropy at half filling and derive an asymptotic approximation thereof by studying the model's continuous limit, which turns out to describe a massless Dirac fermion on a suitably curved background. We show that the leading behavior of the entropy is that of a $c=1$ critical system, although there is a subleading $\log(\log N)$ correction (where $N$ is the number of sites) unusual in this type of models.
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