Title: A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model,
Abstract: The spin transport in isotropic Heisenberg model in the sector with zero
magnetization is generically super-diffusive. Despite that, we here demonstrate
that for a specific set of domain-wall-like initial product states it can
instead be diffusive. We theoretically explain the time evolution of such
states by showing that in the limiting regime of weak spatial modulation they
are approximately product states for very long times, and demonstrate that even
in the case of larger spatial modulation the bipartite entanglement entropy
grows only logarithmically in time. In the limiting regime we derive a simple
closed equation governing the dynamics, which in the continuum limit and for
the initial step magnetization profile results in a solution expressed in terms
of Fresnel integrals.