Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group
Open accessAbstract
We study the recently developed Density Matrix Renormalization Group (DMRG) algorithm in the context of quantum chemistry. In contrast to traditional approaches, this algorithm is believed to yield arbitrarily high accuracy in the energy with only polynomial computational effort. We describe in some detail how this is achieved. We begin by introducing the principles of the renormalization procedure, and how one formulates an algorithm for use in quantum chemistry. The renormalization group algorithm is then interpreted in terms of familiar quantum chemical concepts, and its numerical behavior, including its convergence and computational cost, are studied using both model and real systems. The asymptotic convergence of the algorithm is derived. Finally, we examine the performance of the DMRG on widely studied chemical problems, such as the water molecule, the twisting barrier of ethene, and the dissociation of nitrogen. In all cases, the results compare favorably with the best existing quantum chemical methods, and particularly so when the nondynamical correlation is strong. Some perspectives for future development are given.
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In certain cases DMRG can reach the exact FCI limit.
“In certain cases it can reach the exact FCI limit 115,117 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [117]
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- Authors
- Chan, G. K.-L., & Head-Gordon, M.
- Affiliations
- University of California, Berkeley (US)
- Department of Chemistry, University of California, Berkeley, California 94720-1460
- ORCID
- Chan, Garnet Kin-Lic
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 2002-03-15
- Volume
- 116
- Issue
- 11
- Pages
- 4462-4476
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W1986037653
- Cited by
- 554
- References
- 28
- Citations by year
- 2026: 22 · 2025: 36 · 2024: 22 · 2023: 25 · 2022: 42 · 2021: 38 · 2020: 42 · 2019: 52 · 2018: 41 · 2017: 34 · 2016: 36 · 2015: 30 · 2014: 27 · 2013: 10 · 2012: 14
- FWCI
- 5.34
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Journal of Chemical Physics (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Funders
- Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- density matrix renormalization group, quantum chemistry, renormalization group, asymptotic convergence, strongly correlated electrons, water molecules, nitrogen dissociation, electronic structure
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