Spin transport in antiferromagnets in one and two dimensions calculated using the Kubo formula

We study spin transport in one- and two-dimensional Heisenberg antiferromagnets. In one dimension we take spin S=1. The longitudinal spin conductivity is calculated using the Kubo formula. The magnetic properties of low-dimensional systems are significantly modified by strong correlations effects. The models studied here show unconventional transport behavior: the computed spin conductivity exhibits a nonzero Drude weight at finite temperatures and thus a ballistic character. We present results for the regular part of the conductivity as a function of the frequency.