Persistence of Locality in Systems with Power-Law Interactions
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Motivated by recent experiments with ultracold 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, whereas 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 verified in a variety of ultracold-atomic and solid-state systems.
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Two MPS with different bond dimensions do not belong to the same manifold, so this cannot easily be captured in a smooth differential equation.
“As two MPS with different bond dimensions do not belong to the same manifold [35], this idea cannot easily be captured in a smooth evolution described using a differential equation.”
From Unifying time evolution and optimization with matrix product states (2016) · cites this paper as [35]
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Research works printed but not linked: 2
- B. Nachtergaele and R. Sims, arXiv:1004.2086. · arXiv
- See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.113.030602 for the generalization of our main result Eq. (2) to 2D and 3D lattices.
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- Authors
- Gong, Z.-X., Foss-Feig, M., Michalakis, S., & Gorshkov, A. V.
- Affiliations
- California Institute of Technology (US)
- Joint Quantum Institute (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2014-07-16
- Volume
- 113
- Issue
- 3
- Pages
- 030602-030602
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1997288266
- Cited by
- 122
- References
- 40
- Citations by year
- 2026: 4 · 2025: 1 · 2024: 4 · 2023: 5 · 2022: 8 · 2021: 10 · 2020: 17 · 2019: 19 · 2018: 12 · 2017: 14 · 2016: 13 · 2015: 11 · 2014: 4
- FWCI
- 6.97
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (GBMF1250)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Keywords
- locality, long-range interactions, power-law interactions, information dissemination, ultracold atoms, XY chain, transverse-field Ising chain, local quench, lattice dynamics
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