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Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters

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.