Marginal CFT perturbations at the integer quantum Hall transition

TL;DR

This paper proposes a specific conformal field theory model for the integer quantum Hall transition, analyzes its perturbations and RG flow, and computes physical quantities like conductance at criticality.

Contribution

It introduces a deformed level-4 Wess-Zumino-Novikov-Witten model as the CFT for the transition and studies its marginal perturbations and RG behavior.

Findings

Perturbations are marginal, leading to a non-standard RG flow.

Operator product expansion is used to compute RG-beta functions.

Mean dissipative conductance at fixed point is calculated.

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.