Matrix product states represent ground states faithfully
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We quantify how well matrix product states approximate exact ground states of one-dimensional quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density operators of translational invariant systems. The results give a theoretical justification for the high accuracy of renormalization group algorithms and justifies their use even in the case of critical systems.
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Toric code states and ground states of several 1D spin systems are examples of simulatable states.
“Further interesting examples of simulatable states include the toric code states 92 and the ground states of several 1D spin systems 93 .”
From Measurement-based quantum computation (2009) · cites this paper as [93]
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- Authors
- Verstraete, F., & Cirac, J. I.
- Affiliations
- California Institute of Technology (US)
- Max Planck Institute of Quantum Optics (DE)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2006-03-20
- Volume
- 73
- Issue
- 9
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2066972040
- Cited by
- 730
- References
- 37
- Citations by year
- 2026: 32 · 2025: 58 · 2024: 48 · 2023: 26 · 2022: 38 · 2021: 62 · 2020: 67 · 2019: 40 · 2018: 27 · 2017: 33 · 2016: 35 · 2015: 45 · 2014: 32 · 2013: 28 · 2012: 26
- FWCI
- 16.72
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Gordon and Betty Moore Foundation
- 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 › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- matrix product states, ground state, one-dimensional quantum spin systems, renormalization group, critical systems, translation invariance, block entropy, convex sets, approximation accuracy
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