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On Next-Nearest-Neighbor Interaction in Linear Chain. II
Abstract
Continuing our work on the ground-state properties of the Hamiltonian H=12J ∑ i=1N σi·σi+1 + 12Jα ∑ i=1N σi·σi+2, −1≤α≤1,we have completed the study of 10 spins. The results of short-chain calculations provide better upper and lower bounds of the ground-state energy per particle as N → ∞, but no simple formula can be fitted to the data to get this limit for all α. For J > 0 and α = ½, however, this is exactly found to be −¾J. Some upper and lower bounds for the free energy are also derived.
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Citations
Cited by
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745
Rigorous results on valence-bond ground states in antiferromagnets
Affleck, I., Kennedy, T., Lieb, E. H., & Tasaki, H. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.799 · Cited by 2,223
Rigorous Results on Valence-Bond Ground States in Antiferromagnets
Affleck, I., Kennedy, T., Lieb, E. H., & Tasaki, H. (2004) · Condensed Matter Physics and Exactly Soluble Models · doi:10.1007/978-3-662-06390-3_18 · Cited by 989
Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains
den Nijs, M., & Rommelse, K. (1989) · Physical Review B · doi:10.1103/physrevb.40.4709 · Cited by 936
Vector chiral and multipolar orders in the spin-12frustrated ferromagnetic chain in magnetic field
Hikihara, T., Kecke, L., Momoi, T., & Furusaki, A. (2008) · Physical Review B · doi:10.1103/physrevb.78.144404 · Cited by 306
Metadata
- Authors
- Majumdar, C. K., & Ghosh, D. K.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1969-08-01
- Volume
- 10
- Issue
- 8
- Pages
- 1399-1402
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W4235284319
- Cited by
- 492
- References
- 0
- FWCI
- 0.86
- Type
- journal article
- Language
- en
- Open access
- closed
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- Majumdar, C. K., & Ghosh, D. K. (1969). On Next-Nearest-Neighbor Interaction in Linear Chain. II. Journal of Mathematical Physics. https://doi.org/10.1063/1.1664979
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