Density of states of disordered Dirac particles: Infinitely many operators with negative scaling dimensions and freezing transitions

Abstract

The global density of states (GDOS) close to the band center $\epsilon=0$ for a particle hopping on a square lattice and subjected to disorder that preserves the bipartite symmetry of the lattice is computed using field theoretical methods. The GDOS diverges like $ |\epsilon|^{-1}\exp (-c|\ln\epsilon|^{\kappa} ) $ with $\kappa=2/3$ in agreement with a prediction by Motrunich \textit{et al.} and in disagreement with an older prediction by Gade ($\kappa=1/2$).