Termination of Multifractal Behaviour for Critical Disordered Dirac Fermions

TL;DR

This paper provides an exact solution for disordered Dirac fermions interacting with a non-Abelian potential, revealing a termination of multifractal scaling and correcting previous replica-based results.

Contribution

It introduces a conformal field theory approach that accurately describes the multifractal behavior of disordered Dirac fermions, challenging prior replica method findings.

Findings

Multifractal scaling terminates at a finite order.

Exact conformal field theory solution obtained.

Previous replica solutions are shown to be incorrect for higher correlations.

Abstract

We consider Dirac fermions interacting with a disordered non-Abelian vector potential. The exact solution is obtained through a special type of conformal field theory including logarithmic correlators, without resorting to the replica or supersymmetry approaches. It is shown that the proper treatment of the conformal theory leads to a different multifractal scaling behaviour than initially expected. Moreover, the previous replica solution is found to be incorrect at the level of higher correlation functions.