Multifractality at Anderson transitions with Coulomb interaction

TL;DR

This paper investigates how Coulomb interactions influence the multifractal properties of local density of states near localization transitions in disordered electronic systems, revealing that multifractality persists despite interactions.

Contribution

It provides the first calculation of the multifractal spectrum in interacting disordered systems near localization transitions, highlighting differences from non-interacting cases.

Findings

Multifractality of LDOS survives with Coulomb interaction.

Multifractal spectrum differs from non-interacting systems.

Results are relevant for STM experiments on disordered materials.

Abstract

We explore mesoscopic fluctuations and correlations of the local density of states (LDOS) near localization transition in a disordered interacting electronic system. It is shown that the LDOS multifractality survives in the presence of Coulomb interaction. We calculate the spectrum of multifractal dimensions in $2+\epsilon$ spatial dimensions and show that it differs from that in the absence of interaction. The multifractal character of fluctuations and correlations of the LDOS can be studied experimentally by scanning tunneling microscopy of two-dimensional and three-dimensional disordered structures.