  We investigate the quantum dynamics of site diluted S=1/2 Heisenberg
antiferromagnetic clusters at the percolation threshold. We use Lanczos
diagonalization to calculate the lowest excitation gap Delta and, to reach
larger sizes, study an upper bound for Delta obtained from sum rules involving
the staggered structure factor and susceptibility, which we evaluate by quantum
Monte Carlo simulations. Scaling the gap distribution with the cluster length
L, Delta sim 1/L^z, we obtain a dynamic exponent z approximate 2D_f, where
D_f=91/48 is the fractal dimensionality of the percolating cluster. This is in
contrast to previous expectations of z=D_f. We argue that the low-energy
excitations are due to weakly coupled effective moments formed due to local
imbalance in sublattice occupation.
