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We study the Anderson-Hubbard model in the Hartree-Fock approximation and theexact diagonalization under the coexistence of short-range interaction anddiagonal disorder. We show that there exist unconventional soft gaps, where thesingle-particle (SP) density of states (DOS) $A$ follows a scaling in energy$E$ as $A(E)\propto \exp[-(-\gamma\log |E-E_F|)^d]$ irrespective of electronfilling and long-range order. Here, $d$ is the spatial dimension, $E_F$ theFermi energy and $\gamma$ a non-universal constant. We propose a multi-valleyenergy landscape as their origin. Possible experiments to verify the presenttheory are proposed.

Soft Hubbard gaps in disordered itinerant models with short-range interaction