Entanglement entropy of free fermions on directed graphs
Department of Theoretical Physics and Astrophysics, University of Tabriz, 51664, Tabriz, Iran
* e-mail: F.Egbali@tabrizu.ac.ir
Accepted: 24 November 2017
Published online: 22 December 2017
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2017