Anderson localization and quantum Hall effect: Numerical observation of two-parameter scaling

Werner, Miklós Antal and Brataas, A. and von Oppen, F. and Zaránd, Gergely Attila (2015) Anderson localization and quantum Hall effect: Numerical observation of two-parameter scaling. PHYSICAL REVIEW B, 91 (12). ISSN 2469-9950

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Abstract

A two-dimensional disordered system of noninteracting fermions in a homogeneous magnetic field is investigated numerically. By using a modified Landau gauge, we explore the renormalization group flow of the longitudinal and Hall conductances 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 scaling parameter is also demonstrated in the level curvature distribution. Near the critical point the distribution slightly differs from the prediction 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.

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