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

Themaximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated1-4 andhowdifficult the systemwill be to describe numerically5. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations towithina linear effective 'light cone'6.However, little isknown 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 chainHamiltonian and a variable-rangeXY spin chainHamiltonian to a far-from-equilibrium quantummany-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 coneandmeasure the velocity withwhichcorrelations propagate through the system. This work opens the possibility for studying a wide range of many-body dynamics in quantumsystems that are otherwise intractable. © 2014 Macmillan Publishers Limited. All rights reserved.