Localization and Quantum Percolation

Electronic wave functions are studied on dilute lattices, at dimensionalities $1<~d<~8$. Generalized average inverse participation ratios are expanded in powers of the bond concentration, $p$. $Dlog$ Padé approximants indicate that these ratios diverge as ${(p_q-p)}^{{\gamma }_q}$, signaling the appearance of extended states for $p>\mathrm{}{p}_q$. These Anderson transitions occur above classical percolation. No divergence is detected at $d=2\mathrm{}$. These results are consistent with the existence of localized states at the center of the band.