Density of states for the π-flux state with bipartite real random hopping only:: A weak disorder approach -: art. no. 064202

Gade [Nucl. Phys. B 398, 499 (1993)] has shown that the density of states for a particle hopping on a two-dimensional bipartite lattice in the presence of weak disorder and in the absence of time-reversal symmetry (chiral unitary universality class) is anomalous in the vicinity of the band center epsilon=0 whenever the disorder preserves the sublattice symmetry. More precisely, using a nonlinear sigma model that encodes the sublattice (chiral) symmetry and the absence of time-reversal symmetry she argues that the disorder average density of states diverges as \epsilon\(-1)exp(-c\lnepsilon\(kappa)) with c some nonuniversal positive constant and kappa=1/2 a universal exponent. Her analysis has been extended to the case when time-reversal symmetry is present (chiral orthogonal universality class) for which the same exponent kappa=1/2 was predicted. Motrunich [Phys. Rev. B 65, 064206 (2002)] have argued that the exponent kappa=1/2 does not apply to the density of states in the chiral orthogonal universality class. They predict that kappa=2/3 instead. We confirm the analysis of Motrunich within a field theory for two flavors of Dirac fermions subjected to two types of weak uncorrelated random potentials: a purely imaginary vector potential and a complex valued mass potential. This model is the naive continuum limit of a model describing a particle hopping on a square lattice in the background of a pi-flux phase and subjected to weak disorder that preserves the sublattice symmetry and time-reversal invariance. By commonly held universality arguments, this model is believed to belong to the chiral orthogonal universality class. Our calculation relies in an essential way on the existence of infinitely many local composite operators with negative anomalous scaling dimensions.