S. Sachdev et K. Damle, LOW-TEMPERATURE SPIN-DIFFUSION IN THE ONE-DIMENSIONAL QUANTUM O(3) NONLINEAR SIGMA-MODEL, Physical review letters, 78(5), 1997, pp. 943-946
An effective, low temperature, classical model for spin transport in t
he one-dimensional, gapped, quantum O(3) nonlinear sigma model is deve
loped. Its correlators are obtained by a mapping to a model solved ear
lier by Jepsen. We obtain universal functions for the ballistic-to-dif
fusive crossover and the value of the spin diffusion constant, and the
se are claimed to be exact at low temperatures. Implications for exper
iments on one-dimensional insulators with a spin gap are noted.