Exact Multifractality for Disordered N-Flavour Dirac Fermions in Two Dimensions

TL;DR

This paper provides an exact, nonperturbative calculation of multifractal exponents for two-dimensional disordered Dirac fermions with non-Abelian gauge interactions, demonstrating wavefunction delocalization at strong disorder.

Contribution

It introduces a conformal field theory-based Gaussian model to compute multifractal spectra for arbitrary fermion flavors in a nonperturbative manner.

Findings

Multifractal exponents are exactly calculated at strong disorder.

Wavefunctions remain delocalized despite strong disorder.

Results are valid for any number of fermionic flavors.

Abstract

We present a nonperturbative calculation of all multifractal scaling exponents at strong disorder for critical wavefunctions of Dirac fermions interacting with a non-Abelian random vector potential in two dimensions. The results, valid for an arbitrary number of fermionic flavours, are obtained by deriving from Conformal Field Theory an effective Gaussian model for the wavefunction amplitudes and mapping to the thermodynamics of a single particle in a random potential. Our spectrum confirms that the wavefunctions remain delocalized in the presence of strong disorder.