Marginal CFT perturbations at the integer quantum Hall transition

Abstract

According to recent arguments by the author, the conformal field theory (CFT) describing the scaling limit of the integer quantum Hall plateau transition is a deformed level-4 Wess-Zumino-Novikov-Witten model with Riemannian target space inside a complex Lie supergroup GL. After a summary of that proposal and some of its predictions, the leading irrelevant and relevant perturbations of the proposed CFT are discussed. Argued to be marginal, these result in a non-standard renormalization group (RG) flow near criticality, which calls for modified finite-size scaling analysis and may explain the long-standing inability of numerical work to reach agreement on the values of critical exponents. The technique of operator product expansion is used to compute the RG-beta functions up to cubic order in the couplings. The mean value of the dissipative conductance at the RG-fixed point is calculated for a cylinder geometry with any aspect ratio.

arXiv comment24 pages, no figures

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• Scaling collapse of longitudinal conductance near the integer quantum Hall transition
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• Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics
• On currents in the $O(n)$ loop model
• Random Magnetic Field and the Dirac Fermi Surface