Mesoscopic fluctuations of the single-particle Green's function at Anderson transitions with Coulomb interaction

TL;DR

This paper investigates the multifractal mesoscopic fluctuations of the single-particle Green's function at Anderson transitions with Coulomb interaction, using advanced field-theoretic methods to extend noninteracting results.

Contribution

It constructs pure scaling operators in the interacting Finkel'stein nonlinear sigma model and calculates their anomalous dimensions within a two-loop approximation.

Findings

Pure scaling operators exhibit multifractal behavior.

Anomalous dimensions of these operators are determined.

Results extend understanding of fluctuations in interacting disordered systems.

Abstract

Using the two-loop analysis and the background field method we demonstrate that the local pure scaling operators without derivatives in the Finkel'stein nonlinear sigma model can be constructed by straightforward generalization of the corresponding operators for the noninteracting case. These pure scaling operators demonstrate multifractal behavior and describe mesoscopic fluctuations of the single-particle Green's function. We determine anomalous dimensions of all such pure scaling operators in the interacting theory within the two-loop approximation.