Spin diffusion in a perturbed isotropic Heisenberg spin chain

The isotropic Heisenberg chain represents a particular case of an integrable many-body system exhibiting superdiffusive spin transport at finite temperatures. Here, we show that this model has distinct properties also at finite magnetization m not equal 0, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant D-0(Delta) on the spin anisotropy Delta, with a pronounced maximum at Delta = 1. The latter dependence remains true also in the zero magnetization sector, with superdiffusion at Delta = 1 that is remarkably stable against isotropic perturbation (at least in finite-size systems), consistent with recent experiments with cold atoms.