Generalized multifractality in the spin quantum Hall symmetry class with interaction

TL;DR

This paper investigates how interactions influence the generalized multifractality at the Anderson transition in the spin quantum Hall class, revealing that interactions alter symmetry relations and scaling behaviors.

Contribution

It introduces a framework for analyzing interaction effects on multifractality in class C using the Finkel'stein nonlinear sigma model and computes anomalous dimensions via two-loop RG analysis.

Findings

Interactions modify the anomalous dimensions of scaling operators.

Interaction breaks symmetry relations between multifractal exponents.

Results provide insights into the interplay of disorder, topology, and interactions.

Abstract

Scaling of various local observables with a system size at Anderson transition criticality is characterized by a generalized multifractality. We study the generalized multifractality in the spin quantum Hall symmetry class (class C) in the presence of interaction. We employ Finkel'stein nonlinear sigma model and construct the pure scaling derivativeless operators for class C in the presence of interaction. Within the two-loop renormalization group analysis we compute the anomalous dimensions of the pure scaling operators and demonstrate that they are affected by the interaction. We find that the interaction breaks exact symmetry relations between generalized multifractal exponents known for a noninteracting problem.