Multifractality and electron-electron interaction at Anderson transitions

TL;DR

This paper investigates how multifractal behavior of the local density of states persists in disordered electronic systems with electron-electron interactions near Anderson transitions, providing theoretical spectra of multifractal exponents.

Contribution

It extends the understanding of multifractality at Anderson transitions by including Coulomb interactions and calculating the spectrum of exponents in various symmetry classes.

Findings

Multifractality survives Coulomb interactions near metal-insulator transitions.

Spectrum of multifractal exponents differs with interaction presence.

Results align qualitatively with recent experimental observations.

Abstract

Mesoscopic fluctuations and correlations of the local density of states are studied near metal-insulator transitions in disordered interacting electronic systems. We show that the multifractal behavior of the local density of states survives in the presence of Coulomb interaction. We calculate the spectrum of multifractal exponents in $2+\epsilon$ spatial dimensions for symmetry classes characterized by broken (partially or fully) spin-rotation invariance and show that it differs from that in the absence of interaction. We also estimate the multifractal exponents at the Anderson metal-insulator transition in 2D systems with preserved spin-rotation invariance. Our results for multifractal correlations of the local density of states are in qualitative agreement with recent experimental findings.