Singular density of states of disordered Dirac fermions in chiral models

The Dirac fermion in the random chiral models is studied, which includes the random gauge field model and the random hopping model. We focus on a connection between continuum and lattice models to give a clear perspective for the random chiral models. Two distinct structures of density of states around zero energy, one is a power-law dependence on energy in the inter-mediate energy range and the other is a peak at zero energy, are revealed by an extensive numerical study for large systems up to 250 x 250. For the random hopping model, the above findings reconcile previous inconsistencies between the lattice and the continuum models.