Abstract
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.
Highlights
As a probe in particular of the correlations in quantum many body systems and field theories, the study of entanglement is of fundamental interest
The commuting operator will be found by extending the algebraic Heun operator construction to the framework of the Terwilliger algebra arising in the context of association schemes
Because of the presence of degeneracies, it will call for an extension of the algebraic Heun construction to the framework of Terwilliger algebras [35] which have been introduced to study the properties of association schemes
Summary
As a probe in particular of the correlations in quantum many body systems and field theories, the study of entanglement is of fundamental interest. The commuting operator will be found by extending the algebraic Heun operator construction to the framework of the Terwilliger algebra arising in the context of association schemes This will generalize previous entanglement studies of free Fermion chains [29,9,10,4,5], that exploited ideas borrowed from time and band limiting problems [33,23,34,13,15]. Because of the presence of degeneracies, it will call for an extension of the algebraic Heun construction to the framework of Terwilliger algebras [35] which have been introduced to study the properties of association schemes Put these algebras are generated by the adjacency matrix which plays in our models the role of the Hamiltonian and the orthogonal projectors Ei∗ on subspaces spanned by the characteristic vectors corresponding to the vertices at distance i from the reference one.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
