Propagation of correlations in quantum lattice systems

Bruno Nachtergaele; Yoshiko Ogata; Robert Sims

doi:10.1007/s10955-006-9143-6

Propagation of correlations in quantum lattice systems

Bruno Nachtergaele, Yoshiko Ogata, Robert Sims

Research output: Contribution to journal › Article › peer-review

128 Scopus citations

Abstract

We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics.

Original language	English (US)
Pages (from-to)	1-13
Number of pages	13
Journal	Journal of Statistical Physics
Volume	124
Issue number	1
DOIs	https://doi.org/10.1007/s10955-006-9143-6
State	Published - Jul 2006

Keywords

Correlations
Lieb-Robinson bounds
Quantum spin systems

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-006-9143-6

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keywords = "Correlations, Lieb-Robinson bounds, Quantum spin systems",

author = "Bruno Nachtergaele and Yoshiko Ogata and Robert Sims",

note = "Funding Information: This article is based on work supported by the U.S. National Science Foundation under Grant # DMS-0303316. Y.O. is supported by the Japan Society for the Promotion of Science. We would like to acknowledge Frank Verstraete for posing the questions, the answers to which form the basis of this short note.",

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AU - Sims, Robert

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N2 - We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics.

AB - We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics.

KW - Correlations

KW - Lieb-Robinson bounds

KW - Quantum spin systems

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Propagation of correlations in quantum lattice systems

Abstract

Keywords

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