



01399nas a2200157   4500008004100000245006700041210006600108260001400174490000800188520091600196100001901112700002301131700002501154700002501179856003701204       2014                        eng d00aPersistence of locality in systems with power-law interactions0 aPersistence of locality in systems with powerlaw interactions  c2014/7/160 v1133 a  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.
1 aGong, Zhe-Xuan1 aFoss-Feig, Michael1 aMichalakis, Spyridon1 aGorshkov, Alexey, V.  uhttp://arxiv.org/abs/1401.6174v2