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A simple and commonly employed approximate technique with which one canexamine spatially disordered systems when strong electronic correlations arepresent is based on the use of real-space unrestricted self-consistentHartree-Fock wave functions. In such an approach the disorder is treatedexactly while the correlations are treated approximately. In this report wecritique the success of this approximation by making comparisons between suchsolutions and the exact wave functions for the Anderson-Hubbard model. Due tothe sizes of the complete Hilbert spaces for these problems, the comparisonsare restricted to small one-dimensional chains, up to ten sites, and a 4x4two-dimensional cluster, and at 1/2 filling these Hilbert spaces contain about63,500 and 166 million states, respectively. We have completed thesecalculations both at and away from 1/2 filling. This approximation is based ona variational approach which minimizes the Hartree-Fock energy, and we havecompleted comparisons of the exact and Hartree-Fock energies. However, in orderto assess the success of this approximation in reproducing ground-statecorrelations we have completed comparisons of the local charge and spincorrelations, including the calculation of the overlap of the Hartree-Fock wavefunctions with those of the exact solutions. We find that this approximationreproduces the local charge densities to quite a high accuracy, but that thelocal spin correlations, as represented by < S_i . S_j >, are not as wellrepresented. In addition to these comparisons, we discuss the properties of thespin degrees of freedom in the HF approximation, and where in thedisorder-interaction phase diagram such physics may be important.

Critiquing Variational Theories of the Anderson-Hubbard Model: Real-Space Self-Consistent Hartree-Fock Solutions