Spin diffusion and the spin-1/2XXZchain atT=∞from exact diagonalization

We study the long time behavior of the $\mathrm{zz}$ and $\mathrm{xx}$ time-dependent autocorrelation function of the spin-1/2 $\mathrm{XXZ}$ chain at $T=\infty$ by exact diagonalizations on a chain of 16 sites. We find that the numerical results for the $\mathrm{zz}$ correlation are very well fit by the formula $t^{-d}\left[{A+Be}^{-\gamma \left(t-t_0\right)}\cos \Omega \right(t-t_0\left)\right].$ From this we estimate $d$ as a function of the anisotropy of the chain and study the crossover from ballistic to diffusive behavior.