Spin transport in disordered long-range interacting spin chain

Using a numerically exact technique we study spin transport and entanglement growth in the delocalized phase of a disordered spin chain with long-range interactions, decaying as a power law, r-α with distance. For all considered α's and disorder strengths we find that the entanglement entropy grows sublinearly, and the underlying transport is subdiffusive. Since rare-blocking regions, which are central to the Griffiths theory of transport in disordered interacting systems, can be easily circumvented by long-range hops across the lattice, they cannot explain the mechanism of slow transport in long-range systems. Specifically, we show that for long-range systems the Griffiths theory predicts diffusive transport, which is inconsistent with our results.