Anderson Localization and Quantum Hall Effect: Numerical Observation of Two Parameter Scaling

Abstract

A two dimensional disordered system of non-interacting fermions in a homogeneous magnetic field is investigated numerically. By introducing a new magnetic gauge, we explore the renormalization group (RG) flow of the longitudinal and Hall conductances with higher precision than previously studied, and find that the flow is consistent with the predictions of Pruisken and Khmelnitskii. The extracted critical exponents agree with the results obtained by using transfer matrix methods. The necessity of a second parameter is also reflected in the level curvature distribution. Near the critical point the distribution slightly differs from the prediciton of random matrix theory, in agreement with previous works. Close to the quantum Hall fixed points the distribution is lognormal since here states are strongly localized.

6 pages, 7 figures

References in corpus (9)

• Surface quantized anomalous Hall current and magneto-electric effect in magnetically disordered topological insulators
• Imaging currents in HgTe quantum wells in the quantum spin Hall regime
• Direct imaging of topological edge states in cold-atom systems
• Critical exponent for the quantum Hall transition
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
• Quantum criticality at the Chern-to-normal insulator transition
• Characterization of the Quantized Hall Insulator Phase in the Quantum Critical Regime
• Anti-Levitation in the Integer Quantum Hall Systems

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