title: Non-local propagation of correlations in quantum systems with long-range interactions.
abstract: 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 correlated and how difficult the system will be to describe numerically. 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'. 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 bound 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.
authors.affiliation: Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
authors.forename: Philip
authors.initials: P
authors.lastname: Richerme
authors.affiliation: Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
authors.forename: Zhe-Xuan
authors.initials: ZX
authors.lastname: Gong
authors.affiliation: Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
authors.forename: Aaron
authors.initials: A
authors.lastname: Lee
authors.affiliation: Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
authors.forename: Crystal
authors.initials: C
authors.lastname: Senko
authors.affiliation: Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
authors.forename: Jacob
authors.initials: J
authors.lastname: Smith
authors.affiliation: Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Foss-Feig
authors.affiliation: Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Spyridon
authors.initials: S
authors.lastname: Michalakis
authors.affiliation: Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
authors.forename: Alexey V
authors.initials: AV
authors.lastname: Gorshkov
authors.affiliation: Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
authors.forename: Christopher
authors.initials: C
authors.lastname: Monroe