Random hopping fermions on bipartite lattices: Density of states, inverse participation ratios, and their correlations in a strong disorder regime

We study Anderson localization of non-interacting random hopping fermions on bipartite lattices in two dimensions, focusing our attention to strong disorder features of the model. We concentrate ourselves on specific models with a linear dispersion in the vicinity of the band center, which can be described by a Dirac fermion in the continuum limit. Based on the recent renormalization group method developed by Carpentier and Le Doussal for the XY gauge glass model, we calculate the density of states, inverse participation ratios, and their spatial correlations. It turns out that their behavior is quite different from those expected within naive weak disorder approaches.