Singular density of states of disordered Dirac fermions in chiral models

The Dirac fermion in the random chiral models is studied which includes therandom gauge field model and the random hopping model. We focus on a connectionbetween continuum and lattice models to give a clear perspective for the randomchiral models. Two distinct structures of density of states (DoS) around zeroenergy, one is a power-law dependence on energy in the intermediate energyrange and the other is a diverging one at zero energy, are revealed by anextensive numerical study for large systems up to $250\times 250$. For therandom hopping model, our finding of the diverging DoS within very narrowenergy range reconciles previous inconsistencies between the lattice and thecontinuum models.Comment: 4 pages, 4 figure