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 transport process in the presence of long-range couplings that decay algebraically with distance as r −α . While diffusion is recovered for large exponents α > 1.5, longer-ranged couplings with 0.5 < α ≤ 1.5 give rise to effective classical Lévy flights; a random walk with step sizes following a distribution which falls off algebraically at large distances. We investigate this phenomenon in a long-range interacting XY spin chain, conserving 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. As a consequence, autocorrelations show hydrodynamic tails decaying in time as t −1/(2α−1) when 0.5 < α ≤ 1.5. We also extract the associated generalized diffusion constant, and demonstrate that it follows the prediction of classical Lévy flights; quantum many-body effects manifest themselves in an overall time scale depending only weakly on α. Our findings can be readily verified with current trapped ion experiments.of the hydrodynamic tail in the autocorrelation function C(j = 0, t), depends strongly on the long-range exponent arXiv:1909.01351v1 [cond-mat.quant-gas]
We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.
Identifying universal properties of nonequilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system. We experimentally probed the quantum dynamics of 51 individually controlled ions, realizing a long-range interacting spin chain. By measuring space-time–resolved correlation functions in an infinite temperature state, we observed a whole family of hydrodynamic universality classes, ranging from normal diffusion to anomalous superdiffusion, that are described by Lévy flights. We extracted the transport coefficients of the hydrodynamic theory, reflecting the microscopic properties of the system. Our observations demonstrate the potential for engineered quantum systems to provide key insights into universal properties of nonequilibrium states of quantum matter.
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