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We study the interaction driven localization transition, which a recentexperiment in Ga_{1-x}Mn_xAs As has shown to come along with multifractalbehavior of the local density of states (LDoS) and the intriguing persistenceof critical correlations close to the Fermi level. We show that the bulk ofthese phenomena can be understood within a Hartree-Fock treatment ofdisordered, Coulomb-interacting spinless fermions. A scaling analysis of theLDoS correlation demonstrates multifractality with correlation dimensiond_2=1.57, which is significantly larger than at a non-interacting Andersontransition. At the interaction-driven transition the states at the Fermi levelbecome critical, while the bulk of the spectrum remains delocalized up tosubstantially stronger interactions. The mobility edge stays close to the Fermienergy in a wide range of disorder strength, as the interaction strength isfurther increased. The localization transition is concomitant with thequantum-to-classical crossover in the shape of the pseudo-gap in the tunnelingdensity of states, and with the proliferation of metastable HF solutions thatsuggest the onset of a glassy regime with poor screening properties.

Multifractality and quantum-to-classical crossover in the Coulomb anomaly at the Mott-Anderson metal-insulator transition