Series expansion study of quantum percolation on the square lattice

We study the site and bond quantum percolation model on the two-dimensional square lattice using series expansion in the low concentration limit. We c alculate series for the averages of Sigma(ij) r(ij)(k)T(ij)(E), where T-ij( E) is the transmission coefficient between sites i and j, for k = 0, 1,..., 5 and for several values of the energy E near the center of the band. In t he bond case the series are of order p(14) in the concentration p (some of those have been formerly available to order p(10)) and in the site case of order p(16) The analysis, using the Dlog-Pade approximation and the techniq ues known as M1 and M2, shows clear evidence for a delocalization transitio n (from exponentially localized to extended or power-law-decaying states) a t an energy-dependent threshold p,(E) in the range p, < p(q)(E) < 1, confir ming previous results (e.g. p(q)(0.05) = 0.625 +/- 0.025 and 0.740 +/- 0.02 5 for bond and site percolation) but in contrast with the Anderson model. T he divergence of the series for different Ic is characterized by a constant gap exponent, which is identified as the localization length exponent v fr om a general scaling assumption. We obtain estimates of v = 0.57 +/- 0.10. These values violate the bound v greater than or equal to 2/d of Chayes et al.