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.

广义多重分形表征了在安德森定位临界点处的本征态可观察量的缩放。我们探索了 2D 系统中的广义多重分形，主要关注对称类 C 超导体中的自旋量子霍尔 (SQH) 跃迁。还研究了与传统整数量子霍尔 (IQH) 跃迁的关系和差异。使用非线性 sigma 模型的场论形式主义，我们推导出代表泛化多重分形的纯标度算子，然后将它们“翻译”为本征态可观察量的语言。对 SQH 和 IQH 转换的网络模型进行数值模拟，我们确认了缩放可观察量的分析预测并确定相应的指数。值得注意的是，