Strong disorder effects of a Dirac fermion with a random vector field

TL;DR

This paper investigates the effects of strong disorder on a Dirac fermion with a random vector field, deriving a unified renormalization group framework that explains numerical results and reveals a freezing transition.

Contribution

It introduces a novel approach using bosonization and the KPP equation to analyze strong disorder effects in Dirac fermions, connecting analytical results with numerical findings.

Findings

Derived scaling equations for coupling constants with nonlinear terms

Calculated density of states and inverse participation ratios

Identified the freezing transition in the disorder regime

Abstract

We study a Dirac fermion model with a random vector field, especially paying attention to a strong disorder regime. Applying the bosonization techniques, we first derive an equivalent sine-Gordon model, and next average over the random vector field using the replica trick. The operator product expansion based on the replica action leads to scaling equations of the coupling constants (``fugacities'') with nonlinear terms, if we take into account the fusion of the vertex operators. These equations are converted into a nonlinear diffusion equation known as the KPP equation. By the use of the asymptotic solution of the equation, we calculate the density of state, the generalized inverse participation ratios, and their spatial correlations. We show that results known so far are all derived in a unified way from the point of view of the renormalization group. Remarkably, it turns out that the scaling exponent obtained in this paper reproduces the recent numerical calculations of the density correlation function. This implies that the freezing transition has actually revealed itself in such calculations.