Level statistics and localization in a two-dimensional quantum percolation problem

Abstract

A two-dimensional model for quantum percolation with variable tunnelling range is studied. For this purpose the Lifshitz distribution is considered where the disorder enters the Hamiltonian via the non-diagonal hopping elements. We employ a numerical method to analyse the level statistics of this model. It turns out that the level repulsion is strongest around the percolation threshold. As we go away from the maximum level repulsion a cross-over from a Gaussian orthogonal ensemble type of behaviour to a Poisson-like distribution is revealed. The localization properties are calculated by using the sensitivity to boundary conditions and we find a cross-over from localized to delocalized states.