Freiburg 2019 – scientific programme
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FM: Fall Meeting
FM 56: Entanglement: Many-Body Dynamics II
FM 56.6: Talk
Wednesday, September 25, 2019, 15:30–15:45, 2004
Non-local emergent hydrodynamics in a long-range interacting spin system — •Alexander Schuckert1,2, Izabella Lovas1,2, and Michael Knap1,2 — 1Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München
Short-range interacting quantum systems with a conserved quantity exhibit universal diffusive behavior at late times in the absence of long-lived quasiparticle excitations. We show how this universality is replaced by a more general transport process in the presence of long-range interactions that decay algebraically with distance as r−α. While diffusion is recovered for large exponents α>1.5, longer-ranged interactions with 0.5<α≤1.5 give rise to effective classical Lévy flights; a random walk with step sizes following a heavy-tailed distribution. We investigate this phenomenon in a long-range interacting XY spin chain, conserving the energy and the total magnetization, 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. Moreover, autocorrelations show hydrodynamic tails decaying in time as t−1/(2α−1) when 0.5<α≤1.5. Our findings can be readily verified with current trapped ion experiments.