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

We study the interaction-driven localization transition, which a recent experiment (Richardella et al 2010 Science 327 665) in Ga1−xMnxAs has shown to come along with the 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 (HF) treatment of disordered, Coulomb-interacting spinless fermions. A scaling analysis of the LDoS correlation demonstrates multifractality with the correlation dimension d2 1.57, which is significantly larger than at a non-interacting Anderson transition and is compatible with the experimental value dexp2 = 1.8 ± 0.3. 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.