Entanglement entropy of free fermions on directed graphs

Abstract

In this paper, we study the general spinless quadratic fermion Hamiltonian with interaction matrices given by the symmetric and antisymmetric parts of the adjacency matrix of a directed graph. The correlation matrix and entanglement entropy are provided for the ground state of the Hamiltonian, analytically. We also show that a volume law scaling holds for some scalable sets of nonsymmetric association-scheme graphs. The scaling of the entanglement entropy is then used as a tool for studying the graph isomorphism problem, in particular to distinguish some nonisomorphic pairs of directed strongly regular graphs.