Eur. Phys. J. Plus (2017) 132: 539
https://doi.org/10.1140/epjp/i2017-11805-1

Regular Article

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

Received: 14 June 2017
Accepted: 24 November 2017
Published online: 22 December 2017

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.