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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 (β \to 0). We particularly focus on diffusion and the quantitative evaluation of diffusion constants from current autocorrelations as a function of the anisotropy parameter Δ 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 Δ. The resulting diffusion constants scale as 1/Δ^2 in the Markovian regime Δ<<1 (s=1/2) and as 1/Δ in the highly non-Markovian regime above Δ \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 Δ>1 which are obtained directly from the exact diagonalization of autocorrelations or have been obtained from non-equilibrium bath scenarios.