  We study the Anderson-Hubbard model in the Hartree-Fock approximation and the
exact diagonalization under the coexistence of short-range interaction and
diagonal disorder. We show that there exist unconventional soft gaps, where the
single-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 electron
filling and long-range order. Here, $d$ is the spatial dimension, $E_F$ the
Fermi energy and $\gamma$ a non-universal constant. We propose a multi-valley
energy landscape as their origin. Possible experiments to verify the present
theory are proposed.
