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

TL;DR

This paper calculates the global density of states near zero energy for disordered Dirac particles on a bipartite lattice, revealing a divergence pattern that supports recent theoretical predictions over older ones.

Contribution

It provides a field theoretical computation of the GDOS near the band center, confirming a specific divergence form with a new exponent.

Findings

GDOS diverges as |psilon|^{-1} exp(-c | psilon|^{2/3})

Results agree with Motrunich et al.'s prediction

Disagrees with Gade's earlier prediction

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 ($\kappa=1/2$).