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    Modular invariance, universality and crossover in the quantum Hall effect


    Dolan, Brian P. (1999) Modular invariance, universality and crossover in the quantum Hall effect. Nuclear Physics B, 554 (3). pp. 487-513. ISSN 0550-3213

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    Abstract

    An analytic form for the conductivity tensor in crossover between two quantum Hall plateaux is derived, which appears to be in good agreement with existing experimental data. The derivation relies on an assumed symmetry between quantum Hall states, a generalisation of the law of corresponding states from rational filling factors to complex conductivity, which has a mathematical expression in terms of an action of the modular group on the upper-half complex conductivity plane. This symmetry implies universality in quantum Hall crossovers. The assumption that the β-function for the complex conductivity is a complex analytic function, together with some experimental constraints, results in an analytic expression for the crossover, as a function of the external magnetic field.

    Item Type: Article
    Keywords: Quantum Hall effect; Modular group; Renormalisation group flow; Critical point; Crossover;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 10496
    Identification Number: https://doi.org/10.1016/S0550-3213(99)00326-0
    Depositing User: Dr. Brian Dolan
    Date Deposited: 18 Feb 2019 14:13
    Journal or Publication Title: Nuclear Physics B
    Publisher: Elsevier
    Refereed: Yes
    URI:

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