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Persistence of locality in systems with power-law interactions



Zhexuan Gong, Michael S. Foss-Feig, Spyridon Michalakis, Alexey Gorshkov


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 and decays exponentially in space, reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at long distances. We demonstrate that these two contributions not only bound but qualitatively reproduce the short and long distance dynamical behavior following a local quench in an XY chain and a transverse eld Ising chain. In addition to providing an accurate description of dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally veri ed with a variety of ultracold atomic and solid-state systems.
Physical Review Letters


quantum quench, Lieb-Robinson bound, quantum spin model, non-equilibrium, quantum dynamics


Gong, Z. , Foss-Feig, M. , Michalakis, S. and Gorshkov, A. (2014), Persistence of locality in systems with power-law interactions, Physical Review Letters, [online],, (Accessed May 18, 2024)


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Created July 15, 2014, Updated October 12, 2021