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 (\eta)-pairing method can be employed to construct its exact eigenstates. We arrive at this condition by finding that the requirement for the (\eta)-pairing state ((\eta^\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 ((\eta^\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 ((\eta^\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.