Exact Eigenstates of the Hubbard Model Independent of the On-Site Electron Interaction

Two-dimensional Hubbard model is important to understand the high temperature superconductivity. We give several methods to construct exact eigenstates of the two-dimensional Hubbard model that are independent of the on-site electron interaction. The number of electrons in some eigenstates can be of the order of the lattice sites. It is shown that the existence of eigenstates independent of the electron interactions is a common feature of the extended Hubbard models that have short-range interactions, and some eigenstates we construct can be used to represent eigenstates of the two-dimensional Bose–Hubbard model.