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Quantum percolation transition in 3d: 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 $α_q$, have been determined in the range of $0\leq q\leq 1$. 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 $ν=1.622\pm 0.035$. The mulifractal function, $f(α)$, appears to be universal, however, the exponents $D_q$ and $α_q$ produced anomalous variations along the phase boundary, $p_c^Q(E)$.