Quantum percolation transition in three dimensions: Density of states, finite-size scaling, and multifractality

The phase diagram of the metal-insulator transition in a three-dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large-scale numerical simulation has been performed on systems with linear sizes up to L = 140. The multifractal dimensions, exponents D-q and alpha(q), have been determined in the range of 0 <= q <= 1. Our results confirm that this problem belongs to the same universality class as the three-dimensional Anderson model; the critical exponent of the localization length was found to be nu = 1.622 +/- 0.035. However, the multifractal function f(alpha) and the exponents D-q and alpha(q) produced anomalous variations along the phase boundary, p(c)(Q) (E).