Generalized multifractality at spin quantum Hall transition
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.
- Publication:
-
Annals of Physics
- Pub Date:
- December 2021
- DOI:
- 10.1016/j.aop.2021.168584
- arXiv:
- arXiv:2107.06414
- Bibcode:
- 2021AnPhy.43568584K
- Keywords:
-
- Anderson localization;
- Generalized multifractality;
- Spin quantum Hall effect;
- Non-linear sigma-model;
- Conformal invariance;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- doi:10.1016/j.aop.2021.168584