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Non-local propagation of correlations in quantum systems with long-range interactions

Nature volume 511, pages 198201 (10 July 2014) | Download Citation


The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated1,2,3,4 and how difficult the system will be to describe numerically5. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective ‘light cone’6. However, little is known about the propagation speed in systems with long-range interactions, because analytic solutions rarely exist and because the best long-range bound7 is too loose to accurately describe the relevant dynamical timescales for any known spin model. Here we apply a variable-range Ising spin chain Hamiltonian and a variable-range XY spin chain Hamiltonian to a far-from-equilibrium quantum many-body system and observe its time evolution. For several different interaction ranges, we determine the spatial and time-dependent correlations, extract the shape of the light cone and measure the velocity with which correlations propagate through the system. This work opens the possibility for studying a wide range of many-body dynamics in quantum systems that are otherwise intractable.

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We thank J. Preskill, A. M. Rey, K. Hazzard, A. Daley, J. Schachenmayer, M. Kastner, S. Manmana and L.-M. Duan for discussions. This work is supported by the US Army Research Office (ARO) Award W911NF0710576 with funds from the DARPA Optical Lattice Emulator Program, ARO award W911NF0410234 with funds from the IARPA MQCO Program, and the US NSF Physics Frontier Center at JQI. M.F.-F. thanks the NRC for support. S.M. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontier Center with the support of the Gordon and Betty Moore Foundation (through grant GBMF1250).

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  1. Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA

    • Philip Richerme
    • , Zhe-Xuan Gong
    • , Aaron Lee
    • , Crystal Senko
    • , Jacob Smith
    • , Michael Foss-Feig
    • , Alexey V. Gorshkov
    •  & Christopher Monroe
  2. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA

    • Spyridon Michalakis


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Experiments and data analysis were performed by P.R., A.L., C.S., J.S. and C.M. Theoretical calculations were done by Z.-X.G., M.F.-F., S.M., and A.V.G. All authors contributed to the preparation of the manuscript.

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The authors declare no competing financial interests.

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Correspondence to Philip Richerme.

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