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Persistence of locality in systems with power-law interactions

Gong, Zhe-Xuan and Foss-Feig, Michael and Michalakis, Spyridon and Gorshkov, Alexey V. (2014) Persistence of locality in systems with power-law interactions. Physical Review Letters, 113 (3). Art. No. 030602. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20140717-131453801

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Abstract

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^α interactions with α > 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, 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 verifed in a variety of ultracold-atomic and solid-state systems.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1401.6174v2arXivArticle
http://dx.doi.org/10.1103/PhysRevLett.113.030602DOIArticle
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.030602PublisherArticle
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.030602#supplementalPublisherSupplemental Material
Additional Information:© 2014 American Physical Society. Received 24 January 2014; Published 16 July 2014. Z.-X. G. and M. F.-F. contributed equally to this work. We thank J. Preskill for asking whether the bound derived in Ref. [8] reduces to the nearest-neighbor case as α → ∞, and M. Kastner for pointing out that, if one optimizes with respect to μ at ever r and t in Eq. (2), the hybrid exponential-algebraic behavior shown in Fig. 4 becomes evident only at larger values of α. We thank A. M. Rey, K. Hazzard, C. Monroe, L.-M. Duan, C. Senko, P. Richerme, M. Maghrebi, A. Daley, J. Schachenmayer, A. Lee, J. Smith, and S. Manmana for discussions. This work was supported by the JQI and the NSF PFC at JQI. M. F.-F. thanks the NRC for support. S. M. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
JQI-NSF-PFCUNSPECIFIED
NRC UNSPECIFIED
NSF, Physics Frontier Center, Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Classification Code:PACS numbers: 05.50.+q, 03.65.Ud, 05.70.Ln, 75.10.Pq
Record Number:CaltechAUTHORS:20140717-131453801
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20140717-131453801
Official Citation:Gong, Z.-X., Foss-Feig, M., Michalakis, S., & Gorshkov, A. V. (2014). Persistence of Locality in Systems with Power-Law Interactions. Physical Review Letters, 113(3), 030602.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:47301
Collection:CaltechAUTHORS
Deposited By: Jacquelyn O'Sullivan
Deposited On:19 Jul 2014 17:06
Last Modified:27 Feb 2018 22:18

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