SPECTRAL SIGNATURE OF QUANTUM SPIN-DIFFUSION IN DIMENSIONS D = 1, 2, AND 3

The spectral densities of dynamical spin autocorrelation functions at infinite temperature are studied for the S = 1/2 XXZ model (with exchange couplings J(x) = J(y) = J, J(z)) on the linear chain, the square lattice, and the simple cubic lattice. The low-frequency behavior of a given spectral density is inferred from certain characteristic properties of its continued-fraction coefficients as determined from computed frequency moments. The analysis yields estimates for the J(z)/J dependence of the infrared-singularity exponent. In the d = 1 case, the exponent for spin fluctuations perpendicular to the O(2) symmetry axis responds sensitively as the anisotropy parameter sweeps across the O(3) symmetry point J(z)/J = 1, while the exponent for the parallel fluctuations shows little variation. In the cases d = 2 and d = 3 the same observations are made for autocorrelation functions of aggregate spins in chains and lattice planes, respectively.