Perturbation theory of the Hubbard Hamiltonian on a 4×4 cluster of the square lattice

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Abstract
The ground-state wave function and energy are calculated for the one-band Hubbard Hamiltonian on a 4×4 cluster of the square lattice up to first and second order of the on-site Coulomb repulsion U, respectively. Changes induced by a deviation of the number of electrons from half-filling (one electron per lattice site) are closely followed. Charge-charge and spin-spin correlation functions are directly obtained from the ground-state wave function and show the existence of antiferromagnetic correlations that extend over the whole cluster at half-filling. Correlations among sites separated by more than a lattice site diminish very rapidly as holes are introduced into the cluster. The analysis is extended to the negative-U case. Ground-state properties change qualitatively.