  We study the interaction driven localization transition, which a recent
experiment in Ga_{1-x}Mn_xAs As has shown to come along with multifractal
behavior of the local density of states (LDoS) and the intriguing persistence
of critical correlations close to the Fermi level. We show that the bulk of
these phenomena can be understood within a Hartree-Fock treatment of
disordered, Coulomb-interacting spinless fermions. A scaling analysis of the
LDoS correlation demonstrates multifractality with correlation dimension
d_2=1.57, which is significantly larger than at a non-interacting Anderson
transition. At the interaction-driven transition the states at the Fermi level
become critical, while the bulk of the spectrum remains delocalized up to
substantially stronger interactions. The mobility edge stays close to the Fermi
energy in a wide range of disorder strength, as the interaction strength is
further increased. The localization transition is concomitant with the
quantum-to-classical crossover in the shape of the pseudo-gap in the tunneling
density of states, and with the proliferation of metastable HF solutions that
suggest the onset of a glassy regime with poor screening properties.
