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Cited by 3,244Quantum many-body systemsTheoretical and Computational PhysicsPhysics of Superconductivity and Magnetism

Density-matrix algorithms for quantum renormalization groups

White, Steven R.·1993·Physical Review B
DOI 10.1103/physrevb.48.10345
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Abstract

A formulation of numerical real-space renormalization groups for quantum many-body problems is presented and several algorithms utilizing this formulation are outlined. The methods are presented and demonstrated using S=1/2 and S=1 Heisenberg chains as test cases. The key idea of the formulation is that rather than keep the lowest-lying eigenstates of the Hamiltonian in forming a new effective Hamiltonian of a block of sites, one should keep the most significant eigenstates of the block density matrix, obtained from diagonalizing the Hamiltonian of a larger section of the lattice which includes the block. This approach is much more accurate than the standard approach; for example, energies for the S=1 Heisenberg chain can be obtained to an accuracy of at least ${10}^{\mathrm{\ensuremath{-}}9}$. The method can be applied to almost any one-dimensional quantum lattice system, and can provide a wide variety of static properties.

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Crossref · 10.1103/physrevb.48.10345

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19 of 19 references verified0 citation errors · 0 not checkable

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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 [115]

  • DMRG applied to quantum chemistry can generally handle large active spaces (approximately 50 molecular orbitals).

    “DMRG applied to quantum chemistry can generally handle large active spaces ( ∼ 50 MOs 115 ).”

    From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [115]

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Authors
White, S. R.
Affiliations
University of California, Irvine (US)
Corresponding author
White, Steven R.
ORCID
White, Steven R.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1993-10-01
Volume
48
Issue
14
Pages
10345-10356
ISSN
  • 0163-1829 (ISSN-L)
  • 1095-3795
DOI
10.1103/physrevb.48.10345
OpenAlex
W2016407890
Cited by
3,244
References
19
Citations by year
2026: 126 · 2025: 185 · 2024: 175 · 2023: 153 · 2022: 203 · 2021: 203 · 2020: 160 · 2019: 155 · 2018: 155 · 2017: 156 · 2016: 94 · 2015: 124 · 2014: 110 · 2013: 113 · 2012: 101
FWCI
22.56
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. B, Condensed matter (publishedVersion)
  • PubMed (publishedVersion)
Funders
University of California, Irvine
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 › Condensed Matter Physics › Physics of Superconductivity and Magnetism
Keywords
quantum renormalization group, real-space renormalization group, effective Hamiltonian, Heisenberg spin chain, spin-1/2 chain, quantum many-body systems, static characteristics

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