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    The Modular and Renormalisation Groups in the Quantum Hall Effect

    Dolan, Brian P. (1998) The Modular and Renormalisation Groups in the Quantum Hall Effect. Working Paper.

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    An analytic form for the crossover of the conductivity tensor between two Hall plateaux, as a function of the external magnetic field, is proposed. The form of the crossover is obtained from the action of a symmetry group, a particular subgroup of the modular group, on the upper-half complex conductivity plane, by assuming that the β-function describing the crossover is a holomorphic function of the conductivity. The group action also leads to a selection rule, |p1q2−p2q1| = 1, for allowed transitions between Hall plateaux with filling factors ѵ1 = p1/q1 and ѵ2 = p2/q2, where q1 and q2 are odd.

    Item Type: Monograph (Working Paper)
    Additional Information: Talk presented at the Workshop on the Exact Renormalisation Group, Faro, Portugal, 10-12th September, 1998.
    Keywords: Modular; Renormalisation Groups; Quantum Hall Effect;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 5932
    Identification Number: arXiv:hep-th/9811218
    Depositing User: Dr. Brian Dolan
    Date Deposited: 03 Mar 2015 15:36
    Refereed: Yes
      Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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