Spin transport in disordered long-range interacting spin chain*

We numerically study spin transport and spin-density profiles after a local quench in a disordered one-dimensional spin-chain with long-range interactions, in the regime where delocalization is predicted by all existing theories. We observe a transient super-diffusive transport, followed by asymptotic diffusive behavior. We provide a phenomenological explanation by properly generalized Griffiths picture.