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Anisotropic transport of charge and complexified duality

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Abstract

Charge transport in two dimensions provides an ideal laboratory for investigating parameter space geometries. The Onsager relations for anisotropic transport in a parity-violating external field endow these spaces with a highly nontrivial complex (and Kähler) structure, which can be given a simple geometrical interpretation. A large class of Coulomb gases exhibiting this structure have a generalized Kramers-Wannier symmetry (complexfield duality) which is contained in the modular group. Knowledge of this symmetry and the degrees of freedom encoded in the Coulomb gas appear to be sufficient to determine the global phase diagram and the renormalization group fixed-point structure, including the critical exponents. This accounts for all the scaling behavior observed so far in the quantum Hall system.

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Authors and Affiliations

  1. Department of Physics, University of Oslo, Blindern, P.O. Box 1048, N-0316, Oslo, Norway

    C. A. Lütken

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  1. C. A. Lütken
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Lütken, C.A. Anisotropic transport of charge and complexified duality. J Stat Phys 78, 441–451 (1995). https://doi.org/10.1007/BF02183358

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