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 $ε=0$ 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 $ |ε|^{-1}\exp (-c|\lnε|^κ ) $ with $κ=2/3$ in agreement with a prediction by Motrunich \textit{et al.} and in disagreement with an older prediction by Gade ($κ=1/2$).