Generalized multifractality at spin quantum Hall transition

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