Slater determinant and exact eigenstates of the two-dimensional Fermi-Hubbard model

We consider the construction of exact eigenstates of the two-dimensional Fermi-Hubbard model defined on an L×L lattice with a periodic condition. Based on the characteristics of Slater determinants, several methods are introduced to construct exact eigenstates of the model. The eigenstates constructed are independent of the on-site electron interaction and some of them can also represent exact eigenstates of the two-dimensional Bose-Hubbard model.