Spin transport in a long-range-interacting spin chain

We numerically study spin transport and spin-density profiles after a local quench in a clean one-dimensional spin chain with long-range interactions, decaying as a power law, r-α with distance. We find two distinct regimes of transport: for α<1/2, spin excitations relax instantaneously in the thermodynamic limit, and for α>1/2, spin transport combines both diffusive and superdiffusive features. We show that while for α>3/2 the spin diffusion coefficient is finite, transport in the system is never strictly diffusive, contrary to corresponding classical systems.