The Liouville Theory as a Model for Prelocalized States in Disordered Conductors

TL;DR

This paper demonstrates that the Liouville model effectively describes the distribution of zero energy eigenfunctions in (2+1)-dimensional Dirac electrons under random gauge potential, linking it to localization phenomena in disordered conductors.

Contribution

It establishes a connection between the Liouville model and the behavior of disordered electronic systems, revealing a line of critical points relevant to localization theory.

Findings

Distribution of eigenfunctions matches Liouville model predictions

Scaling dimensions align with conventional localization theory

Renormalization group flow is near Liouville critical points

Abstract

It is established that the distribution of the zero energy eigenfunctions of (2 + 1)-dimensional Dirac electrons in a random gauge potential is described by the Liouville model. This model has a line of critical points parameterized by the strength of disorder and the scaling dimensions of the inverse participation ratios coincide with the dimensions obtained in the conventional localization theory. From this fact we conclude that the renormalization group trajectory of the latter theory lies in the vicinity of the line of critical points of the Liouville model.