Date of Original Version
The spectral densities of dynamical spin autocorrelation functions at infinite temperature are studied for the S = 1/2 XXZ model (with exchange couplings Jx = Jy = J, Jz) 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 Jz/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 Jz/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.
Markus Böhm, Hajo Leschke, Martin Henneke, V.S. Viswanath, Joachim Stolze and Gerhard Müller. Spectral signature of quantum spin diffusion in dimensions d=1,2,3. Phys. Rev. B 49 (1994), 417-421. Available at http://journals.aps.org/prb/abstract/10.1103/PhysRevB.49.417