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Mohammad ali jafarizadeh, Faghiheh Eghbalifam, Susan Nami

Entanglement entropy in the ground state of supersymmetric fermion lattice models



2022, Chinese Journal of Physics,

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.
 




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