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Scaling Theory of the Integer Quantum Hall Effect

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arxiv cond-mat/9501106 v1 pith:6ITU7VEX submitted 1995-01-23 cond-mat

Bodo Huckestein This is my paper · ORCID
classification cond-mat
keywords scalinghalllocalizationnumericaltheorytransitionseffectexperimental
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The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the main emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered systems are described in detail. An overview of the finite-size scaling theory and its relation to Anderson localization is given. The field-theoretical approach to the localization problem is outlined. Numerical methods for the calculation of scaling quantities, in particular the localization length, are detailed. The properties of local observables at the localization-delocalization transition are discussed in terms of multifractal measures. Finally, the results of extensive numerical investigations are compared with experimental findings.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 778 citations worldwide. Full citation record

  1. Topological phase transitions between bosonic and fermionic quantum Hall states near even-denominator filling factors

    cond-mat.mes-hall 2025-08 unverdicted novelty 7.0 of 10

    The transition between Jain and daughter quantum Hall states is mapped to an E8 to trivial transition and predicted to split into at least eight transitions with intermediate topological phases.

  2. Coherent and dissipative dynamics at quantum phase transitions

    cond-mat.stat-mech 2021-03 unverdicted novelty 2.0 of 10

    A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.

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