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 $m\ne 0$, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant ${\mathcal{D}}_0\left(\mathrm{\Delta }\right)$ 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.

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• Ballistic transport
• Diffusion
• Dissipative dynamics
• Magnons
• Quantum transport
• Spin dynamics
• 1-dimensional spin chains
• Nonequilibrium systems
• Quantum many-body systems
• Quantum spin models
• Strongly correlated systems
• Exact solutions for many-body systems
• Integrable systems
• Lattice models in condensed matter
• Lindblad equation
• Many-body techniques
• Tensor network methods