Entanglement entropy in the ground state of supersymmetric fermion lattice models

In this paper, we study the entanglement entropy for strongly correlated spinless fermions in the ground state of a supersymmetric Hamiltonian on diverse graphs. Then, we use the entanglement entropy to study the graph isomorphism (GI) problem on some non-isomorphic pairs of graphs to distinguish them from each other. The GI problem is considered on pairs of non-isomorphic strongly regular graphs (SRG) and some cases of regular graphs. The SRGs are well-known for being highly symmetric, so that they rarely can be detected by classical and quantum algorithms. However, we show that most of the pairs of non-isomorphic SRGs can be distinguished by utilizing the supersymmetric entanglement entropy. Also, detecting the regular non-isomorphic graphs is often difficult. The obtained result illustrates that the entanglement entropy of the single-particle Hamiltonian cannot detect non-isomorphic pairs of regular graphs, but the entanglement entropy of the two-particle Hamiltonian can.