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

Steinigeweg R, Schnalle R. Projection operator approach to spin diffusion in the anisotropic Heisenberg chain at high temperatures. PHYSICAL REVIEW E. 2010;82(4): 40103.Spin transport in the anisotropic Heisenberg chain is typically investigated theoretically with respect to the finiteness of transport coefficients only. Assuming their finiteness at high temperatures, we develop a concrete quantitative picture of the diffusion constant/(dc-)conductivity as a function of both the anisotropy parameter Delta and the spin quantum number s, going beyond the most commonly considered case s = 1/2. Using this picture, we enable the comparison of finite transport coefficients from complementary theoretical methods on a quantitative level, having more significance than the finiteness alone. Our method is essentially based on an application of the time-convolutionless projection operator technique to current autocorrelations. This technique, although being a perturbation theory in Delta, is found to be applicable, even if Delta is not small. This finding supports the applicability to a wider class of strongly interacting many-particle quantum systems