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Spin transport in the XXZ model at high temperatures: Classical dynamics versus quantum S=1/2 autocorrelations

The transport of magnetization is analyzed for the classical Heisenberg chain at and especially above the isotropic point. To this end, the Hamiltonian equations of motion are solved numerically for initial states realizing harmonic-like magnetization profiles of small amplitude and with random phases. Above the isotropic point, the resulting dynamics is observed to be diffusive in a hydrodynamic regime starting at comparatively small times and wave lengths. In particular, hydrodynamic regime and diffusion constant are both found to be in quantitative agreement with close-to-equilibrium results from quantum S=1/2 autocorrelations at high temperatures. At the isotropic point, the resulting dynamics turns out to be non-diffusive at the considered times and wave lengths.