Spin diffusion in 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 $m\mathrm{\ne }0$, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant ${\mathcal{D}}_0(\mathrm{\Delta })$ on the spin anisotropy $\mathrm{\Delta }$, with a pronounced maximum at $\mathrm{\Delta }=1$. The latter dependence remains true also in the zero magnetization sector, with superdiffusion at $\mathrm{\Delta }=1$ that is remarkably stable against isotropic perturbation (at least in finite-size systems), consistent with recent experiments with cold atoms.