GAP FORMATION AND PHASE-DIAGRAM OF THE DISORDERED HUBBARD-MODEL IN THE ALLOY-ANALOGY APPROXIMATION

We study the gap for one-particle excitations as a function of the on-site repulsion U and the disorder W in the disordered Hubbard model in two and three dimensions. We consider the half-filled band case in the paramagnetic phase of this model. The analysis is done within the alloy-analogy approximation using the localized-eigenstates approximation to calculate the density of states. We find that there is a critical U(c) for a gap opening at the Fermi level in both two and three dimensions. This allows us to determine a phase diagram of the model that separates a Mott-Hubbard insulating phase and an unspecified gapless phase. The critical U(c) line grows with disorder and tends to be linear for large enough W. Our results are consistent with previous real-space renormalization-group studies.