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

TL;DR

This paper investigates the interaction-driven localization transition in disordered Coulomb systems, revealing multifractality, a quantum-to-classical crossover, and signs of glassy behavior near the Mott-Anderson transition.

Contribution

It provides a Hartree-Fock based analysis of multifractality and critical states at the transition, highlighting the persistence of critical correlations and the emergence of glassy features.

Findings

Multifractality with correlation dimension d_2=1.57 at the transition

Critical states at the Fermi level coexist with delocalized bulk states

Localization transition coincides with a quantum-to-classical crossover and glassy regime

Abstract

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.