Localization length exponent in two models of quantum Hall plateau transitions

Abstract

Motivated by the recent numerical studies on the Chalker-Coddington network model that found a larger-than-expected critical exponent of the localization length characterizing the integer quantum Hall plateau transitions, we revisited the exponent calculation in the continuum model and in the lattice model, both projected to the lowest Landau level or subband. Combining scaling results with or without the corrections of an irrelevant length scale, we obtain $\nu =2.48\pm 0.02$, which is larger but still consistent with the earlier results in the two models, unlike what was found recently in the network model. The scaling of the total number of conducting states, as determined by the Chern number calculation, is accompanied by an effective irrelevant length scale exponent $y=4.3$ in the lattice model, indicating that the irrelevant perturbations are insignificant in the topology number calculation.

arXiv comment10 pages, 8 figures

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Cited by in corpus (30)

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• Modular Commutators in Conformal Field Theory
• Random network models with variable disorder of geometry
• Fractional Chern insulators with a non-Landau level continuum limit
• Evolution of Berry curvature and reentrant quantum anomalous Hall effect in an intrinsic magnetic topological insulator
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• Scaling collapse of longitudinal conductance near the integer quantum Hall transition
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• Marginal CFT perturbations at the integer quantum Hall transition
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• Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions
• Green's functions on a renormalized lattice: An improved method for the integer quantum Hall transition
• Composite Fermion Nonlinear Sigma Models
• Topology and many-body localization
• Localization renormalization and quantum Hall systems
• Critical behavior at the integer quantum Hall transition in a network model on the Kagome lattice
• The integer quantum Hall transition: an $S$-matrix approach to random networks
• Irrelevant corrections at the quantum Hall transition
• Quantum Hall criticality in an amorphous Chern insulator
• Localization and interactions in topological and non-topological bands in two dimensions
• Random Magnetic Field and the Dirac Fermi Surface
• Edge state critical behavior of the integer quantum Hall transition
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• The impact of dimensionality on universality of quantum Hall transitions