论文标题
不均匀的XX旋转链和准可溶模型
Inhomogeneous XX spin chains and quasi-exactly solvable models
论文作者
论文摘要
我们建立了不均匀的XX旋转链（或自由的fermion系统跳跃）与线上的某些QES模型之间的联系，从而产生了一个弱正交多项式的家族。我们对所有此类模型及其相关的XX链进行了分类，其中包括两个与Lamé（有限间隙）量子潜力有关的家庭。对于其中一个链条，我们通过数值计算了半填充的rényi二分纠缠熵，并通过研究模型的连续极限来得出其渐近近似，这证明了在适当弯曲的背景上描述一个无质量的dirac fermion。我们表明，熵的领先行为是$ c = 1 $关键系统的领先行为，尽管在这种类型的型号中有一个转向的$ \ log（\ log n）$校正（其中$ n $是网站数）。
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.
