SPIN-DIFFUSION IN THE ONE-DIMENSIONAL S = 1/2 XXZ MODEL AT INFINITE TEMPERATURE

Time-dependent spin-autocorrelation functions at T = infinity and (in particular) their spectral densities for the bulk spin and the boundary spin of the semi-infinite spin-1/2 XXZ model (with exchange parameters J(x) = J(y) = J, J(z)) are investigated on the basis of (i) rigorous bounds in the time domain and (ii) a continued-fraction analysis in the frequency domain. We have found strong numerical evidence for spin diffusion in quantum spin models. For J(z)/J increasing from zero, the results of the short-time expansion indicate a change of the bulk-spin xx-autocorrelation function from Gaussian decay to exponential decay. The continued-fraction analysis of the same dynamic quantity signals a change from exponential decay to power-law decay as J(z)/J approaches unity and back to a more rapid decay upon further increase of that parameter. By contrast, the change in symmetry at J(z)/J = 1 has virtually no impact on the bulk-spin zz-autocorrelation function (as expected). Similar contrasting properties are observable in the boundary-spin autocorrelation functions.