Free Fermions on vertices of distance-regular graphs are considered. Bipartitions 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 detail 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.

考虑距离规则图的顶点上的自由费米子。通过将距参考折点给定距离的所有折点取为一部分来定义等分。基态是通过填充低于某个能量的所有状态来构造的。从时间和频带限制问题，代数Heun算符和Terwilliger代数中借用了概念，它显示了如何大致上获得与纠缠哈密顿量交换的块三对角矩阵。在该框架内详细研究了Hadamard图的情况，并显示了交换矩阵的存在，以便对受限的两点相关矩阵进行解析对角化，从而明确确定纠缠熵。