Localization in two-dimensional quantum percolation

Abstract

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 scalng theory of localization and in disagreement with recent claims of a localization transition in two dimensions. The localization length λ is given by exp{B[p/(1-p)${]}^{\mathit{y}}$} with y very close to 0.5 and p the probability that a site or a bond is present.