We consider magnetotransport in high-mobility 2D electron gas in a non-quantizing magnetic field. We employ a weakly chiral network model to test numerically the prediction of the scaling theory that the transition from an Anderson to a quantum Hall insulator takes place when the Drude value of the non-diagonal conductivity is equal to 1/2. The weaker is the magnetic field the harder it is to locate a delocalization transition using quantum simulations. The main idea of the present study is that the position of the transition does not change when a strong local inhomogeneity is introduced. Since the strong inhomogeneity suppresses interference, transport reduces to classical percolation. We show that the corresponding percolation problem is bond percolation over two sublattices coupled to each other by random bonds. Simulation of this percolation allows to access the domain of very weak magnetic fields. Simulation results confirm the criterion σ_{xy}=1/2 for values σ_{xx}\sim 10, where they agree with earlier quantum simulation results. However for larger σ_{xx} we find that the transition boundary is described by σ_{xy} σ_{xx}^k with k= 0.5, i.e., the transition takes place at higher magnetic fields. The strong inhomogeneity limit of magnetotransport in the presence of a random magnetic field, pertinent to composite fermions, corresponds to a different percolation problem. In this limit we find for the delocalization transition boundary σ_{xy} σ_{xx}^{0.6}.
Generalized multifractality at the spin quantum Hall transition: Percolation mapping and pure-scaling observables
本文推广了二维无序超导体自旋量子霍尔跃迁临界本征态的广义多重分形分析[J. F. Karcher等人，Annals of Physics，435，168584（2021）]。一个映射到经典渗流的广义多重分形可观的一组特定的。这样，相应的指数的准确的分析结果得到。此外，正的纯标度本征函数观测量的一般结构，这允许一个非常有效的数值确定标度指数。特别是，所有指数对应的多项式纯缩放可观的顺序$q=5$的数字。对于导出的渗流映射的观测量，分析和数值结果是完全一致的。分析和数值结果清楚地表明，广义抛物线（即，与二次Casimir算子的本征值成比例）对于广义多重分形指数的谱不成立。这排除了Wess-Zumino-Novikov-Witten模型，以及更一般的，任何具有局部共形不变性的理论，作为自旋量子霍尔跃迁的定点理论的候选者。在这项工作中开发的可观察的建设铺平了道路，调查广义多重分形在安德森本地化的临界点的各种对称类。
Percolation from Quantum Metric in Flat-Band Delocalization
Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
