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We investigate the quantum dynamics of site diluted S=1/2 Heisenbergantiferromagnetic clusters at the percolation threshold. We use Lanczosdiagonalization to calculate the lowest excitation gap Delta and, to reachlarger sizes, study an upper bound for Delta obtained from sum rules involvingthe staggered structure factor and susceptibility, which we evaluate by quantumMonte Carlo simulations. Scaling the gap distribution with the cluster lengthL, Delta sim 1/L^z, we obtain a dynamic exponent z approximate 2D_f, whereD_f=91/48 is the fractal dimensionality of the percolating cluster. This is incontrast to previous expectations of z=D_f. We argue that the low-energyexcitations are due to weakly coupled effective moments formed due to localimbalance in sublattice occupation.Comment: 4 pages,4 figure

physical review letters

Low-Energy Dynamics of the Two-Dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math>Heisenberg Antiferromagnet on Percolating Clusters

Low-Energy Dynamics of the Two-DimensionalS=1/2Heisenberg Antiferromagnet on Percolating Clusters