LOCALIZATION IN 2-DIMENSIONAL QUANTUM PERCOLATION

The quantum site and bond percolation problem, which is defined by a disordered tight-binding Hamiltonian with a binary probability distribution, is studied using finite-size-scaling methods. For the simple square lattice, we find that all states are exponentially localized for any amount of disorder, in agreement with the scaling theory of localization and in disagreement with recent claims of a localization transition in two dimensions. The localization length-lambda is given by A exp{B[p/(1 - p)]y} with y very close to 0.5 and p the probability that a site or a bond is present.