Dynamic spin-pair correlations in a Heisenberg chain at infinite temperature based on an extended short-time expansion

Exact coefficients of the short-time expansion of the spin-pair correlations are computed up to order t 30 in the one-dimensional spin-1/2 Heisenberg model with isotropic nearest-neighbour interaction at infinite temperature. The key points of the computational algorithm are sketched. The newly derived coefficients are used to obtain lower and upper bounds on the pair correlations which are graphically indistinguishable up to time nearly twice as large as those up to which previous bounds are reasonably close together. In view of the spin-diffusion hypothesis the spatial spread of the pair correlations is studied as a function of time, but no indication for a diffusive long-time behaviour is found in the extended time region, where the new bounds provide control.