Boundary multifractality in the spin quantum Hall symmetry class with interaction

TL;DR

This paper investigates how electron-electron interactions affect boundary multifractality at Anderson transitions in the spin quantum Hall class, revealing that interactions double boundary exponents and break certain symmetry relations.

Contribution

It extends the concept of boundary multifractality to interacting systems in the spin quantum Hall class using two-loop RG analysis.

Findings

Boundary multifractal exponents are twice larger than bulk exponents.

Interactions break symmetry relations between boundary multifractal exponents.

The study provides analytical insights into the effects of interactions on boundary critical phenomena.

Abstract

Generalized multifractality characterizes system size dependence of pure scaling local observables at Anderson transitions in all ten symmetry classes of disordered systems. Recently, the concept of generalized multifractality has been extended to boundaries of critical disordered noninteracting systems. Here we study the generalized boundary multifractality in the presence of electron-electron interaction, focusing on the spin quantum Hall symmetry class (class C). Employing the two-loop renormalization group analysis within Finkel'stein nonlinear sigma model we compute the anomalous dimensions of the pure scaling operators located at the boundary of the system. We find that generalized boundary multifractal exponents are twice larger than their bulk counterparts. Exact symmetry relations between generalized boundary multifractal exponents in the case of noninteracting systems are explicitly broken by the interaction.