Frequency-Dependent Self-Correlation Function for the Heisenberg Spin System in One Dimension

Abstract
The exact numerical calculations by Carboni and Richards for S1z(t)S1z(0)(ω) in a one-dimensional Heisenberg system of S=12 spins at elevated temperatures are compared with the predictions of a simple, two-parameter Gaussian representation of the generalized diffusivity. The parameters of the diffusivity are completely determined by the known second and fourth frequency moments, and the procedure is free of arbitrary parameters. The results of the calculation are found to be in good agreement with Carboni and Richards. The calculation is also carried out for S>12, and it is found that with the increase in the magnitude of spin, S1z(t)S1z(0)(ω) gradually loses its characteristic hump and approaches a shape roughly similar to the one which would result from the use of an appropriate Lorentzian for the function Sfz(t)Sgz(0)(k,ω).