Gap formation and phase diagram of the disordered Hubbard model in the alloy-analogy approximation.

Abstract

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 ${\mathit{U}}_{\mathit{c}}$ 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 ${\mathit{U}}_{\mathit{c}}$ line grows with disorder and tends to be linear for large enough W. Our results are consistent with previous real-space renormalization-group studies.