  We examine quantum percolation on a square lattice with random dilution up to
$q=38%$ and energy $0.001 \le E \le 1.6$ (measured in units of the hopping
matrix element), using numerical calculations of the transmission coefficient
at a much larger scale than previously. Our results confirm the previous
finding that the two dimensional quantum percolation model exhibits
localization-delocalization transitions, where the localized region splits into
an exponentially localized region and a power-law localization region. We
determine a fuller phase diagram confirming all three regions for energies as
low as $E=0.1$, and the delocalized and exponentially localized regions for
energies down to $E=0.001$. We also examine the scaling behavior of the
residual transmission coefficient in the delocalized region, the power law
exponent in the power-law localized region, and the localization length in the
exponentially localized region. Our results suggest that the residual
transmission at the delocalized to power-law localized phase boundary may be
discontinuous, and that the localization length is likely not to diverge with a
power-law at the exponentially localized to power-law localized phase boundary.
However, further work is needed to definitively assess the characters of the
two phase transitions as well as the nature of the intermediate power-law
regime.
