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Title:
Numerical evidence for marginal scaling at the integer quantum Hall transition
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Abstract:
The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling behavior near the IQHT has been studied in experiments and numerical simulations. It is notoriously difficult to pin down the precise values of critical exponents, which seem to vary with model details and thus challenge the principle of universality. Recently, Zirnbauer has conjectured a conformal field theory for the transition, in which linear terms in the beta-functions vanish, leading to a very slow flow in the fixed point’s vicinity. In this work, we provide numerical evidence for such a scenario by using extensive simulations of various network models of the IQHT at unprecedented length scales. At criticality, we show that the finite-size scaling of the disorder averaged longitudinal Landauer conductance agrees with expectations from the field theory. Away from criticality we describe a mechanism that could account for the emergence of an effective critical exponent ν_eff, which is necessarily dependent on the parameters of the model. We further support this idea by exact numerical determination of ν_eff in suitably chosen models.
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