paper

Persistence of locality in systems with power-law interactions

arXiv:1401.6174 · doi:10.1103/PhysRevLett.113.030602

Abstract

Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in -dimensional lattice models exhibiting interactions with . 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 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.

5 pages, 4 figures, version accepted by PRL

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