Entanglement in fermionic chains and bispectrality

Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel drawn with the analysis of time band limiting signal processing. It shown that a tridiagonal matrix commuting entanglement Hamiltonian can be found using algebraic Heun operator construct instances when there an underlying bispectral problem. Cases corresponding to Lie algebras $\mathfrak{su}(2)$ $\mathfrak{su}(1,1)$ as well q-deformed algebra $\mathfrak{so}_q(3)$ at $q$ root unity are presented.