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Cited by 264Quantum many-body systemsAdvanced Chemical Physics StudiesQuantum Computing Algorithms and Architecture

Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach

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Legeza, Ö., Röder, J., Hess, B. A.·2003·Physical Review B
DOI 10.1103/physrevb.67.125114
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Abstract

We have applied the momentum space version of the density-matrix renormalization-group method (k-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in this new context. We have shown numerically that it is possible to determine the desired accuracy of the method in advance of the calculations by dynamically controlling the truncation error and the number of block states using a novel protocol that we dubbed dynamical block state selection protocol. The relationship between the real error and truncation error has been studied as a function of the number of orbitals and the fraction of filled orbitals. We have calculated the ground state of the molecules ${\mathrm{CH}}_{2},$ ${\mathrm{H}}_{2}\mathrm{O},$ and ${\mathrm{F}}_{2}$ as well as the first excited state of ${\mathrm{CH}}_{2}.$ Our largest calculations were carried out with 57 orbitals, the largest number of block states was 1500--2000, and the largest dimensions of the Hilbert space of the superblock configuration was 800 000--1 200 000.

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Crossref · 10.1103/physrevb.67.125114

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  • For linear or quasi-linear molecular systems, active spaces of a hundred molecular orbitals are reachable with DMRG.

    “In case of linear (or quasi-linear) molecular systems, active spaces of a hundred of MOs are reachable 118 .”

    From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [118]

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Research works printed but not linked: 1

  1. S. R. White, 1993, Phys. Rev. B, 48, 10

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Related

Authors
Legeza, Ö., Röder, J., & Hess, B. A.
Affiliations
Friedrich-Alexander-Universität Erlangen-Nürnberg (DE)
ORCID
Legeza, Ö.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2003-03-19
Volume
67
Issue
12
ISSN
  • 0163-1829 (ISSN-L)
  • 1095-3795
DOI
10.1103/physrevb.67.125114
OpenAlex
W2081934208
Semantic Scholar
ec419d846edb465bf509e45e3122b708088f92da
Cited by
263
References
29
Citations by year
2026: 6 · 2025: 6 · 2024: 15 · 2023: 10 · 2022: 12 · 2021: 16 · 2020: 20 · 2019: 21 · 2018: 17 · 2017: 15 · 2016: 15 · 2015: 19 · 2014: 16 · 2013: 8 · 2012: 8
FWCI
5.92
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. B, Condensed matter (publishedVersion)
  • arXiv (Cornell University) (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 › Advanced Chemical Physics Studies
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords
density matrix renormalization group, momentum space, truncation error, accuracy control, quantum chemistry, excited states, CH2, water, F2, many-body systems

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