Gaussian free fields at the integer quantum Hall plateau transition

TL;DR

This paper proposes a Gaussian free field model for critical wavefunctions at the integer quantum Hall transition, using conformal field theory to derive a parabolic multifractality spectrum and exact lattice identities.

Contribution

It introduces a novel Gaussian free field description of critical wavefunctions and connects lattice models with conformal field theory insights.

Findings

Multifractality spectrum is parabolic.

Exact lattice identities are derived.

Effective field theory describes critical wavefunctions.

Abstract

In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical wave intensities prepared via point contacts behave as pure scaling fields obeying an Abelian operator product expansion. Our arguments employ the framework of conformal field theory and, in particular, lead to a multifractality spectrum which is parabolic. We also derive a number of old and new identities that hold exactly at the lattice level and hinge on the correspondence between the Chalker-Coddington network model and a supersymmetric vertex model.