We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter $\Delta$ is varied spin transport changes from ballistic for $\Delta <1$ to anomalous at the isotropic point $\Delta =1$, to diffusive for finite $\Delta >1$, ending up as a perfect isolator in the Ising limit of infinite $\Delta$. Using perturbation theory for large $\Delta$ a quantitative prediction is made for the dependence of diffusion constant on $\Delta$.

• Received 23 March 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.220601