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

TL;DR

This paper explores conditions under which eta-pairing states are exact eigenstates in Hubbard models with bond-charge interactions on general graphs, revealing new eigenstates and expanding understanding of such models.

Contribution

It provides a specific condition for eta-pairing states to be eigenstates in these models and identifies additional exact eigenstates beyond the eta-pairing states.

Findings

Derived a condition for eta-pairing states to be eigenstates.

Identified additional exact eigenstates of the Hamiltonian.

Enhanced understanding of Hubbard models with bond-charge interactions.

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.