Quantum diffusion in two-dimensional random systems with particle-hole symmetry

We study the scattering dynamics of an $n$-component spinor wavefunction in a random environment on a two-dimensional lattice. In the presence of particle-hole symmetry we find diffusion on large scales. The latter is described by a non-interacting Grassmann field, indicating a special kind of asymptotic freedom in $d=2$.
Comment: 9 pages, no figures, extended version