Localization effects in quantum percolation

We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focusing on the statistics of the local density of states and the spatial structure of the single particle wave functions. Using the kernel polynomial method we refine previous studies of the metal-insulator transition and demonstrate the nonmonotonic energy dependence of the quantum percolation threshold. Remarkably, the data indicates a “fragmentation” of the spectrum into extended and localized states. In addition, the observation of a chequerboardlike structure of the wave functions at the band center can be interpreted as anomalous localization.