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General Entanglement Scaling Laws from Time Evolution
Open accessAbstract
We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.
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“Indeed, this fact is related to correlation and entanglement spreading according to the Lieb-Robinson theorem that states that, after a sufficiently large time, states can become strongly entangled ([91-96], see also [97]).”
From Can one trust quantum simulators? (2012) · cites this paper as [92]
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- P. Calabrese, J. Stat. Mech., 2004, P002
- 10.1103/PhysRevB.72.045141 · DOI
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“The linear increasing followed by (almost) saturation has been checked in several lattice models both analytically and numerically [113, 53, 125, 126, 127, 128, 129, 124, 130, 131, 132], but we do not have room here to discuss the several interesting features that emerged like power-law behaviour for large time, perio…”
BackgroundQuantum many-body systems out of equilibrium
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Self-citation
Metadata
- Authors
- Eisert, J., & Osborne, T. J.
- Affiliations
- London Institute for Mathematical Sciences (GB)
- Royal Holloway University of London (GB)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-10-12
- Volume
- 97
- Issue
- 15
- Pages
- 150404-150404
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2062419763
- Cited by
- 201
- References
- 49
- Citations by year
- 2026: 4 · 2025: 14 · 2024: 9 · 2023: 4 · 2022: 7 · 2021: 7 · 2020: 8 · 2019: 11 · 2018: 8 · 2017: 7 · 2016: 15 · 2015: 10 · 2014: 12 · 2013: 9 · 2012: 18
- FWCI
- 9.22
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- quantum spin chains, geometric entropy, Lieb-Robinson bound, sudden quench, quantum phase transitions, gapped ground states, fermionic systems, quantum information
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