Spectral signature of quantum spin diffusion in dimensionsd=1, 2, and 3

The spectral densities of dynamical spin autocorrelation functions at infinite temperature are studied for the S=1/2XXZ model (with exchange couplings ${\mathit{J}}_{\mathit{x}}$=${\mathit{J}}_{\mathit{y}}$≡J,${\mathit{J}}_{\mathit{z}}$) 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 ${\mathit{J}}_{\mathit{z}}$/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 ${\mathit{J}}_{\mathit{z}}$/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.