Conformal field theory of the integer quantum Hall plateau transition

TL;DR

This paper proposes a conformal field theory model for the quantum Hall plateau transition, revealing a nonlinear sigma model with a Wess-Zumino-Novikov-Witten term that matches numerical and theoretical constraints.

Contribution

It introduces a novel conformal field theory involving a superspace and a marginal deformation, explaining the critical behavior of the quantum Hall transition.

Findings

The theory matches the classical conductivity sigma_xx=1/2.

Predicts a critical exponent of 2/pi for point-contact conductance.

Identifies a truly marginal deformation affecting universality.

Abstract

A solution to the long-standing problem of identifying the conformal field theory governing the transition between quantized Hall plateaus of a disordered noninteracting 2d electron gas, is proposed. The theory is a nonlinear sigma model with a Wess-Zumino-Novikov-Witten term, and fields taking values in a Riemannian symmetric superspace based on H^3 x S^3. Essentially the same conformal field theory appeared in very recent work on string propagation in AdS_3 backgrounds. We explain how the proposed theory manages to obey a number of tight constraints, two of which are constancy of the partition function and noncriticality of the local density of states. An unexpected feature is the existence of a truly marginal deformation, restricting the extent to which universality can hold in critical quantum Hall systems. The marginal coupling is fixed by matching the short-distance singularity of the conductance between two interior contacts to the classical conductivity sigma_xx = 1/2 of the Chalker-Coddington network model. For this value, perturbation theory predicts a critical exponent 2/pi for the typical point-contact conductance, in agreement with numerical simulations. The irrational exponent is tolerated by the fact that the symmetry algebra of the field theory is Virasoro but not affine Lie algebraic.