Projection operator approach to spin diffusion in the anisotropic Heisenberg chain at high temperatures

We investigate spin transport in the anisotropic Heisenberg chain in the limit of high temperatures ({\beta} \to 0). We particularly focus on diffusion and the quantitative evaluation of diffusion constants from current autocorrelations as a function of the anisotropy parameter {\Delta} and the spin quantum number s. Our approach is essentially based on an application of the time-convolutionless (TCL) projection operator technique. Within this perturbative approach the projection onto the current yields the decay of autocorrelations to lowest order of {\Delta}. The resulting diffusion constants scale as 1/{\Delta}^2 in the Markovian regime {\Delta}<<1 (s=1/2) and as 1/{\Delta} in the highly non-Markovian regime above {\Delta} \sim 1 (arbitrary s). In the latter regime the dependence on s appears approximately as an overall scaling factor \sqrt{s(s+1)} only. These results are in remarkably good agreement with diffusion constants for {\Delta}>1 which are obtained directly from the exact diagonalization of autocorrelations or have been obtained from non-equilibrium bath scenarios.