Eta-pairing states in Hubbard models with bond-charge interactions on general graphs

Abstract

We investigate Hubbard models with bond-charge interactions on general graphs. For a Hamiltonian \(H\) of such a model, we provide the condition on its parameters under which the \(η\)-pairing method can be employed to construct its exact eigenstates. We arrive at this condition by finding that the requirement for the \(η\)-pairing state \((η^\dagger)^N |0\rangle\) to be an eigenstate of \(H\) is identical to the requirement for it to be an eigenstate of a Hubbard-type Hamiltonian \(H_m\). When the condition for \((η^\dagger)^N |0\rangle\) to be an eigenstate of the Hubbard-type Hamiltonian \(H_m\) is satisfied, we demonstrate that there are additional states, distinct from \((η^\dagger)^N |0\rangle\), which are also exact eigenstates of \(H_m\). Our results enhance the understanding of Hubbard models on general graphs, both with and without bond-charge interactions.

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