论文标题
超平面晶格上不均匀的自由费的纠缠
Entanglement of inhomogeneous free fermions on hyperplane lattices
论文作者
论文摘要
我们在$（d-1）$ - 尺寸晶格上引入了一种不均匀的自由费，并带有$ d（d-1）/2 $连续参数，该参数控制着相邻站点之间的跳跃强度。我们准确地解决了该模型，并发现特征函数是由Krawtchouk多项式的多维概括给出的。我们构建了一个使用切碎的相关矩阵上下班的HEUN操作员，并以$ d = 2,3,4 $的数值计算纠缠熵，对于广泛的参数。对于$ d = 2 $，我们观察到对纠缠熵的子领先贡献的振荡，我们猜想了确切的表达。对于$ d> 2 $，我们发现对纠缠熵的对数违反了对参数的纠缠熵的行为。
We introduce an inhomogeneous model of free fermions on a $(D-1)$-dimensional lattice with $D(D-1)/2$ continuous parameters that control the hopping strength between adjacent sites. We solve this model exactly, and find that the eigenfunctions are given by multidimensional generalizations of Krawtchouk polynomials. We construct a Heun operator that commutes with the chopped correlation matrix, and compute the entanglement entropy numerically for $D=2,3,4$, for a wide range of parameters. For $D=2$, we observe oscillations in the sub-leading contribution to the entanglement entropy, for which we conjecture an exact expression. For $D>2$, we find logarithmic violations of the area law for the entanglement entropy with nontrivial dependence on the parameters.
