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Cited by 247Quantum many-body systemsPhysics of Superconductivity and MagnetismQuantum Computing Algorithms and Architecture

Simulating strongly correlated quantum systems with tree tensor networks

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Murg, V., Verstraete, F., Legeza, Ö., Noack, R. M.·2010·Physical Review B
DOI 10.1103/physrevb.82.205105
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Abstract

We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density-matrix renormalization group (DMRG) method have long been applied to such systems, the spatial topology of DMRG-based methods allows efficient optimizations to be carried out with respect to one spatial dimension only. Extending the matrix-product-state picture, we formulate a more general approach by allowing the local sites to be coupled to more than two neighboring auxiliary subspaces. Following [Y. Shi, L. Duan, and G. Vidal, Phys. Rev. A 74, 022320 (2006)], we treat a treelike network ansatz with arbitrary coordination number $z$, where the $z=2$ case corresponds to the one-dimensional (1D) scheme. For this ansatz, the long-range correlation deviates from the mean-field value polynomially with distance, in contrast to the matrix-product ansatz, which deviates exponentially. The computational cost of the tree-tensor-network method is significantly smaller than that of previous DMRG-based attempts, which renormalize several blocks into a single block. In addition, we investigate the effect of unitary transformations on the local basis states and present a method for optimizing such transformations. For the 1D interacting spinless fermion model, the optimized transformation interpolates smoothly between real space and momentum space. Calculations carried out on small quantum chemical systems support our approach.

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  • Nuclear quantum effects are needed for simulating condensed matter systems containing low-temperature helium and hydrogen, and for high-accuracy simulations of hydrogen-containing room-temperature systems such as liquid water.

    “Nuclear quantum effects are needed for simulating condensed matter systems containing low-temperature helium and hydrogen 143 , as well as for obtaining high accuracy simulations of hydrogen-containing room-temperature systems such as liquid water 144 .”

    From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [144]

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Research works printed but not linked: 2

  1. G. Barcza, Ö. Legeza, K. Marti, and M. Reiher, arXiv:1008.4607 ͑unpublished͒. · arXiv
  2. H. G. Luo, M. P. Qin, and T. Xiang, arXiv:1002.1287 ͑unpub- lished͒. · arXiv

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Authors
Murg, V., Verstraete, F., Legeza, Ö., & Noack, R. M.
Affiliations
University of Vienna (AT)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2010-11-03
Volume
82
Issue
20
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.82.205105
OpenAlex
W1976879565
Cited by
245
References
62
Citations by year
2026: 11 · 2025: 23 · 2024: 22 · 2023: 14 · 2022: 12 · 2021: 22 · 2020: 27 · 2019: 19 · 2018: 19 · 2017: 10 · 2016: 10 · 2015: 9 · 2014: 16 · 2013: 14 · 2012: 11
FWCI
5.32
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review B (publishedVersion)
  • Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) (acceptedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords
tree tensor networks, strongly correlated systems, nonlocal interactions, long-range correlations, density matrix renormalization group, matrix product states, coordination number, spinless fermion model, quantum chemistry

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