Time-dependent autocorrelation function for a linear Heisenberg chain at infinite temperature

Numerical calculations have been performed to obtain the exact infinite-temperature time-dependent spin autocorrelation function $G\left(t\right)\mathrm{}$ for a linear chain of $N$ spins ($S=\frac{1}{2}$) interacting by nearest-neighbor Heisenberg exchange for $N=5, 7, 9 \mathrm{and} 11$ by a method different from that of Carboni and Richards. Exact results for the first 20 moments and estimates for $M_{22}$ to $M_{30}$ of the frequency autocorrelation function for the infinite chain are provided. Excellent agreement is obtained with some recent results obtained by Morita, who, however, gives terms only up to $M_{10}$. $G\left(t\right)\mathrm{}$ does not show a simple monotonic diffusive ($\sim t^{-\frac{1}{2}}$) behavior within $\frac{4\hslash }{J}$, the time domain up to which we believe our result for $N=11\mathrm{}$ to be equivalent to that of the infinite chain although it is reduced to about 10% of its value at $t=0\mathrm{}$.