The Hubbard model for small clusters

The Hubbard model with nearest neighbor hopping, and one type of orbital is applied to clusters of 4 and 5 sites. Results are reported for the ground state as a function of the number of electrons. A rather complicated dependence of the spin of the ground state on occupation number, geometry, and model parameters is found. Ground state energies are compared. The excitation spectrum is illustrated in a particular example.