论文标题
hadamard图上的免费费米子的纠缠
Entanglement of Free Fermions on Hadamard Graphs
论文作者
论文摘要
考虑了距离规则图的顶点上的自由费。两部分是通过将所有顶点作为距参考顶点的给定距离的所有顶点的一部分来定义的。基态是通过填充一定能量以下的所有状态来构建的。借用时间和频段限制问题，代数Heun运营商和Terwilliger代数的概念，它表明了如何获得与纠缠汉密尔顿的通勤的块型三角矩阵。在该框架内研究了Hadamard图的情况，并证明了通勤矩阵的存在，以允许对受限制的两点相关矩阵的分析对角线化，因此可以显式确定纠缠熵。
Free Fermions on vertices of distance-regular graphs are considered. Bipartition are defined by taking as one part all vertices at a given distance from a reference vertex. The ground state is constructed by filling all states below a certain energy. Borrowing concepts from time and band limiting problems, algebraic Heun operators and Terwilliger algebras, it is shown how to obtain, quite generally, a block tridiagonal matrix that commutes with the entanglement Hamiltonian. The case of the Hadamard graphs is studied in details within that framework and the existence of the commuting matrix is shown to allow for an analytic diagonalization of the restricted two-point correlation matrix and hence for an explicit determination of the entanglement entropy.
