Lieb-Robinson Light Cone for Power-Law Interactions

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we pre...

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Bibliographic Details
Published in:Physical review letters 2021-10, Vol.127 (16), p.160401-160401, Article 160401
Main Authors: Tran, Minh C., Guo, Andrew Y., Baldwin, Christopher L., Ehrenberg, Adam, Gorshkov, Alexey V., Lucas, Andrew
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
dipolar interaction
lattice models in statistical physics
mathematical physics
Physics
Power law
quantum communication
quantum information processing
Quantum phenomena
quantum state transfer
Speed limits
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Summary:The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we present a definitive answer to this question for all exponents α > 2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α−2d} to propagate a distance r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.127.160401