Spin dynamics for the one-dimensionalXYmodel at infinite temperature

The infinite-temperature space- and time-dependent spin-correlation functions gᵣˣ(t) are studied for the one-dimensional XY model. Numerical calculations are performed to obtain the exact autocorrelation function g₀ˣ(t) for chains containing 5, 7, and 9 spins (S=1/2). This yields exact results for the first 16 moments of the frequency autocorrelation function of the infinite chain, and estimates for a few of the higher moments as well. The analysis suggests that g₀ˣ(t) for the infinite chain is identical to exp(-J²t²)4. We show that gᵣˣ(t) for r≠0 vanishes identically for all values of time, implying a wave-vector-independent relaxation shape function. Our result for g₀ˣ(t) is compared with that obtained by Huber for the classical (S=∞) chain.