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