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We have obtained the exact ground state wave functions of theAnderson-Hubbard model for different electron fillings on a 4x4 lattice withperiodic boundary conditions - for 1/2 filling such ground states have roughly166 million states. When compared to the uncorrelated ground states (Hubbardinteraction set to zero) we have found strong evidence of the very effectivescreening of the charge homogeneities due to the Hubbard interaction. We havesuccessfully modelled these local charge densities using a non-interactingmodel with a static screening of the impurity potentials. In addition, we havecompared such wave functions to self-consistent real-space unrestrictedHartree-Fock solutions and have found that these approximate ground state wavefunctions are remarkably successful at reproducing the local charge densities,and may indicate the role of dipolar backflow in producing a novel metallicstate in two dimensions.

Exact diagonalization analysis of the Anderson-Hubbard model and comparison to real-space self-consistent Hartree-Fock solutions