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 level4 WessZuminoNovikovWitten 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 nonstandard renormalization group (RG) flow near criticality, which calls for modified finitesize scaling analysis and may explain the longstanding inability of numerical work to reach agreement on the values of critical exponents. The technique of operator product expansion is used to compute the RGbeta functions up to cubic order in the couplings. The mean value of the dissipative conductance at the RGfixed point is calculated for a cylinder geometry with any aspect ratio.
 Publication:

Annals of Physics
 Pub Date:
 August 2021
 DOI:
 10.1016/j.aop.2021.168559
 arXiv:
 arXiv:2106.01291
 Bibcode:
 2021AnPhy.43168559Z
 Keywords:

 Conformal field theory;
 WessZuminoNovikovWitten model;
 Operator product expansion;
 Renormalization group flow;
 Currentcurrent correlation function;
 Vortex singularities;
 Mathematical Physics;
 Condensed Matter  Disordered Systems and Neural Networks;
 High Energy Physics  Theory
 EPrint:
 24 pages, no figures