Rigorous results on valence-bond ground states in antiferromagnets
Abstract
We present rigorous results on a phase in antiferromagnets in one dimension and more, which we call a valence-bond solid. The ground state is simply constructed out of valence bonds, is nondegenerate, and breaks no symmetries. There is an energy gap and an exponentially decaying correlation function. Physical applications are mentioned.
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The equally weighted superposition of all different localized valence-bond states corresponds to a quantum spin liquid, the resonating valence-bond state.
“In general, the equally weighted superposition of all different localized valence-bond states corresponds to a quantum spin liquid, the so-called resonating valence-bond state[37, 38].”
From Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems (2011) · cites this paper as [37]
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 [37]
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- Authors
- Affleck, I., Kennedy, T., Lieb, E. H., & Tasaki, H.
- Affiliations
- Princeton University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1987-08-17
- Volume
- 59
- Issue
- 7
- Pages
- 799-802
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2040059039
- Cited by
- 2,223
- References
- 13
- Citations by year
- 2026: 76 · 2025: 91 · 2024: 87 · 2023: 142 · 2022: 97 · 2021: 102 · 2020: 121 · 2019: 90 · 2018: 102 · 2017: 94 · 2016: 83 · 2015: 81 · 2014: 69 · 2013: 60 · 2012: 51
- FWCI
- 18.24
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- valence bond solid, antiferromagnets, one-dimensional spin chain, ground state, band gap, symmetry breaking, rigorous results
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