Spin transport in disordered long-range interacting spin chain

Using a numerically exact technique we study spin transport and the evolution of spin-density excitation profiles in a disordered spin-chain with long-range interactions, decaying as a power-law, $r^{-α}$ with distance and $α<2$. Our study confirms the prediction of recent theories that the system is delocalized in this parameters regime. Moreover we find that for $α>3/2$ the underlying transport is diffusive with a transient super-diffusive tail, similarly to the situation in clean long-range systems. We generalize the Griffiths picture to long-range systems and show that it captures the essential properties of the exact dynamics.

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