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Cited by 214Advanced Condensed Matter PhysicsQuantum many-body systemsPhysics of Superconductivity and Magnetism

Plaquette valence-bond crystal in the frustrated Heisenberg quantum antiferromagnet on the square lattice

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Mambrini, Matthieu, Läuchli, Andreas, Poilblanc, Didier, Mila, Frédéric·2006·Physical Review B
DOI 10.1103/physrevb.74.144422
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Abstract

Using both exact diagonalizations and diagonalizations in a subset of short-range valence-bond singlets, we address the nature of the groundstate of the Heisenberg spin-$1∕2$ antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (${J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ model). A detailed comparison of the two approaches reveals a region along the line $({J}_{2}+{J}_{3})∕{J}_{1}=1∕2$, where the description in terms of nearest-neighbor singlet coverings is excellent, therefore providing evidence for a magnetically disordered region. Furthermore, a careful analysis of dimer-dimer correlation functions, dimer structure factors and plaquette-plaquette correlation functions provides striking evidence for the presence of a plaquette valence bond crystal order in part of the magnetically disordered region.

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  • Tuning the coupling ratio to κ = -∞ results in the equally weighted superposition |Φ×> + |Φ||>, whereas κ = 1 leads to the resonating valence-bond state |Φ=> + |Φ||>.

    “Tuning the coupling ratio to κ = -∞ results in the equally weighted superposition | Φ × 〉 + ∣ ∣ Φ ‖ 〉 , whereas κ = 1 leads to the interesting resonating valence-bond state[37-39] | Φ = 〉 + ∣ ∣ Φ ‖ 〉 .”

    From Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems (2011) · cites this paper as [39]

  • It was conjectured that a transition from a localized valence-bond configuration to the superposition of different valence-bond states might explain high-temperature superconductivity in cuprates.

    “The studies of these states are of high interest, because it was conjectured that a transition from an localized valence-bond configuration to the superposition of different valence-bond states might explain high-temperature superconductivity in cuprates[39].”

    From Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems (2011) · cites this paper as [39]

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Authors
Mambrini, M., Läuchli, A., Poilblanc, D., & Mila, F.
Affiliations
  • Laboratoire de Physique Théorique (FR)
  • École Polytechnique Fédérale de Lausanne (CH)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2006-10-23
Volume
74
Issue
14
Pages
144422
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.74.144422
OpenAlex
W2074833155
Cited by
214
References
34
Citations by year
2026: 2 · 2025: 7 · 2024: 14 · 2023: 9 · 2022: 13 · 2021: 14 · 2020: 13 · 2019: 18 · 2018: 13 · 2017: 7 · 2016: 17 · 2015: 7 · 2014: 13 · 2013: 10 · 2012: 13
FWCI
6.97
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review B (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • HAL (submittedVersion)
  • Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
  • arXiv (Cornell University)
Funders
Agence Nationale de la Recherche
Topics
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
  • 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
Keywords
frustrated Heisenberg antiferromagnet, square lattice, next-nearest-neighbor coupling, spin-1/2 antiferromagnet, magnetic disorder, ground state

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