TY - JOUR
T1 - Non-local propagation of correlations in long-range interacting quantum systems
JF - Nature
Y1 - 2014
A1 - Philip Richerme
A1 - Zhe-Xuan Gong
A1 - Aaron Lee
A1 - Crystal Senko
A1 - Jacob Smith
A1 - Michael Foss-Feig
A1 - Spyridon Michalakis
A1 - Alexey V. Gorshkov
A1 - Christopher Monroe
AB - 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, since the best long-range bound is too loose to give the correct light-cone shape for any known spin model and since analytic solutions rarely exist. In this work, we experimentally determine the spatial and time-dependent correlations of a far-from-equilibrium quantum many-body system evolving under a long-range Ising- or XY-model Hamiltonian. For several different interaction ranges, we extract the shape of the light cone and measure the velocity with which correlations propagate through the system. In many cases we find increasing propagation velocities, which violate the Lieb-Robinson prediction, and in one instance cannot be explained by any existing theory. Our results demonstrate that even modestly-sized quantum simulators are well-poised for studying complicated many-body systems that are intractable to classical computation.
VL - 511
U4 - 198 - 201
UR - http://arxiv.org/abs/1401.5088v1
CP - 7508
J1 - Nature
U5 - 10.1038/nature13450
ER -
TY - JOUR
T1 - Persistence of locality in systems with power-law interactions
JF - Physical Review Letters
Y1 - 2014
A1 - Zhe-Xuan Gong
A1 - Michael Foss-Feig
A1 - Spyridon Michalakis
A1 - Alexey V. Gorshkov
AB - Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, \emph{qualitatively reproduce} the short- and long-distance dynamical behavior following a local quench in an $XY$ chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems.
VL - 113
UR - http://arxiv.org/abs/1401.6174v2
CP - 3
J1 - Phys. Rev. Lett.
U5 - 10.1103/PhysRevLett.113.030602
ER -