Composite fermions with quenched disorder at the half-filled Landau level

The gapless state at the half-filled Landau level is approximately described in terms of nearly-free composite fermions. Within the mean-field approximation, it has recently been shown that the composite fermions describe a quantum phase transition between an insulator and an integer quantum Hall state when the effects of a quenched disorder are included. Here, we further characterize this random quantum critical point using the non-linear sigma model and network model approaches to disordered fermions.