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

Abstract

We study a Dirac fermion model with a random vector field, especially paying attention to the strong disorder regime. Applying Bosonization techniques, we first derive an equivalent sine-Gordon model, and next average over the random vector field using the replica approach. 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 Kolmogorov-Petrovsky-Piscounov (KPP) equation. Using the asymptotic solution of the equation, we calculate the spatial correlations of the generalized inverse participation ratios. The scaling exponent thus obtained reproduces the recent numerical calculations of the density correlation function. This implies that the freezing transition has actually revealed itself in such calculations.