Generalized multifractality at spin quantum Hall transition

TL;DR

This paper investigates generalized multifractality at the spin quantum Hall transition, deriving theoretical operators and confirming their scaling through numerical simulations, revealing violations of conformal invariance.

Contribution

It introduces a field-theoretical framework for generalized multifractality at the SQH transition and compares it with the IQH transition, providing new analytical and numerical insights.

Findings

Generalized multifractality exponents at SQH violate parabolicity.

Numerical simulations confirm analytical predictions.

Violation of local conformal invariance at SQH critical point.

Abstract

Generalized multifractality characterizes scaling of eigenstate observables at Anderson-localization critical points. We explore generalized multifractality in 2D systems, with the main focus on the spin quantum Hall (SQH) transition in superconductors of symmetry class C. Relations and differences with the conventional integer quantum Hall (IQH) transition are also studied. Using the field-theoretical formalism of non-linear sigma-model, we derive the pure-scaling operators representing generalizing multifractality and then "translate" them to the language of eigenstate observables. Performing numerical simulations on network models for SQH and IQH transitions, we confirm the analytical predictions for scaling observables and determine the corresponding exponents. Remarkably, the generalized-multifractality exponents at the SQH critical point strongly violate the generalized parabolicity of the spectrum, which implies violation of the local conformal invariance at this critical point.