Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We show how this universality is replaced by a more general superdiffusive transport process in the presence of long-range interactions, decaying algebraically with distance. While diffusive behavior is recovered for a sufficiently fast decay, longer-ranged couplings give rise to an effective classical Levy flight, a random walk with step sizes following a heavy-tailed distribution. We study this phenomenon in a long-range interacting XY spin chain with conserved total magnetization, at infinite temperature. We investigate the dynamics 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, and show superdiffusive spreading, with scaling functions given by the stable symmetric distributions. We also extract the associated generalized diffusion constant, and demonstrate that it follows the prediction of classical Levy flights; quantum many-body effects manifest themselves in an overall time scale depending only weakly on the precise form of the algebraic long-range interaction. Our findings can be readily verified with current trapped ion experiments.
Non-local emergent hydrodynamics in a long-range quantum spin system
2021. 03. 19. 10:15
Izabella Lovas (TU München)