The maximum speed with which information can propagate in a quantum many-bodysystem directly affects how quickly disparate parts of the system can becomecorrelated and how difficult the system will be to describe numerically. Forsystems with only short-range interactions, Lieb and Robinson derived aconstant-velocity bound that limits correlations to within a linear effectivelight cone. However, little is known about the propagation speed in systemswith long-range interactions, since the best long-range bound is too loose togive the correct light-cone shape for any known spin model and since analyticsolutions rarely exist. In this work, we experimentally determine the spatialand time-dependent correlations of a far-from-equilibrium quantum many-bodysystem evolving under a long-range Ising- or XY-model Hamiltonian. For severaldifferent interaction ranges, we extract the shape of the light cone andmeasure the velocity with which correlations propagate through the system. Inmany cases we find increasing propagation velocities, which violate theLieb-Robinson prediction, and in one instance cannot be explained by anyexisting theory. Our results demonstrate that even modestly-sized quantumsimulators are well-poised for studying complicated many-body systems that areintractable to classical computation.
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