Exact Density of States in a System of Disordered Two Dimensional Dirac Fermions in the Unitarity Limit: The d-wave Superconductor

In this paper we present a method to compute the exact density of states induced by $N$ non magnetic impurities in a system of two dimensional Dirac fermions in the unitarity limit. We review the case of the $\pi$-flux phase of the Heisenberg model and also treat the disordered d-wave superconductor. In both case we find additional states in the gap with $\delta \rho (\omega) \simeq n_i/ |\omega(\ln^2 |\omega/\Delta_0| + (\pi/2)^2)|$.