Disordered Dirac Fermions: Multifractality Termination and Logarithmic Conformal Field Theories

TL;DR

This paper demonstrates that disordered Dirac fermions with non-Abelian potentials are exactly solvable in the strong disorder limit using logarithmic conformal field theory, revealing multifractality termination and correcting prior replica-based results.

Contribution

It provides an exact solution without replicas or supersymmetry, showing multifractality termination and proposing a general mechanism for SU(N) theories.

Findings

Exact solution in the infinite disorder limit as a logarithmic CFT

Termination of the multifractal spectrum due to locality conditions

Previous replica solutions are shown to be incorrect

Abstract

We reexamine in detail the problem of fermions interacting with a non-Abelian random vector potential. Without resorting to the replica or supersymmetry approaches, we show that in the limit of infinite disorder strength the theory possesses an exact solution which takes the form of a logarithmic conformal field theory. We show that the proper treatment of the locality conditions in the SU(2) theory leads to the termination of the multifractal spectrum, or in other words to the termination of the infinite hierarchies of negative-dimensional operators that were thought to occur. Based on arguments of logarithmic degeneracies, we conjecture that such a termination mechanism should be present for general SU(N). Moreover, our results lead to the conclusion that the previous replica solution of this problem yields incorrect results.