Non-local emergent hydrodynamics in a long-range quantum spin system*

Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We show [1] how this universality is extended by effective classical Lévy flights in the presence of long-range couplings that decay algebraically with distance as r^-α for 0.5<α≤1.5. We investigate this phenomenon in a long-range interacting XY spin chain at infinite temperature by employing non-equilibrium quantum field theory and semi classical phase-space simulations. We find that the space-time dependent spin density profiles are self-similar, with scaling functions given by the stable symmetric distributions. Hence, autocorrelations show hydrodynamic tails decaying in time as t^-1/(2α-1). We also extract the associated generalized diffusion constant, and demonstrate that it follows the prediction of Lévy flights; quantum many-body effects manifest themselves in an overall time scale depending only weakly on α. Our findings can be verified with current trapped ion experiments.

[1] Alexander Schuckert, Izabella Lovas, Michael Knap, arXiv: 1909.01351