Nonlocal emergent hydrodynamics in a long-range quantum spin system
Alexander Schuckert, Izabella Lovas, Michael Knap
Abstract
Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ nonequilibrium quantum field theory and semiclassical phase-space simulations to show how this universality is replaced by a more general transport process in a long-range XY spin chain at infinite temperature with couplings decaying algebraically with distance as ${r}^{\ensuremath{-}\ensuremath{\alpha}}$. While diffusion is recovered for $\ensuremath{\alpha}>1.5$, longer-ranged couplings with $0.5<\ensuremath{\alpha}\ensuremath{\le}1.5$ give rise to effective classical L\'evy flights, a random walk with step sizes drawn from a distribution with algebraic tails. We find that the space-time-dependent spin density profiles are self-similar, with scaling functions given by the stable symmetric distributions. As a consequence, for $0.5<\ensuremath{\alpha}\ensuremath{\le}1.5$, autocorrelations show hydrodynamic tails decaying in time as ${t}^{\ensuremath{-}1/(2\ensuremath{\alpha}\ensuremath{-}1)}$ and linear-response theory breaks down. Our findings can be readily verified with current trapped ion experiments.