The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
On Next-Nearest-Neighbor Interaction in Linear Chain. I
Abstract
Ground-state properties of the Hamiltonian H=12J ∑ i=1N σi·σi+1 + 12Jα ∑ i=1N σi·σi+2(σN+1 ≡ σ1, σN+2 ≡ σ2) are studied for both signs of J and −1 ≤ α ≤ 1 to gain insight into the stability of the ground state with nearest-neighbor interactions only (α = 0) in the presence of the next-nearest-neighbor interaction. Short chains of up to 8 particles have been exactly studied. For J > 0, the ground state for even N belongs always to spin zero, but its symmetry changes for certain values of α. For J < 0, the ground state belongs either to the highest spin (ferromagnetic state) or to the lowest spin and so to zero for even N. The trend of the results suggests that these facts are true for arbitrary N and that the critical value of α is probably zero. Upper and lower bounds to the ground-state energy per spin of the above Hamiltonian are obtained. Such bounds can also be obtained for the square lattice with the nearest- as well as the next-nearest-neighbor interaction.
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Cites
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Entanglement in many-body systems
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Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
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Orús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255
Finitely correlated states on quantum spin chains
Fannes, M., Nachtergaele, B., & Werner, R. F. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02099178 · Cited by 1,422
Quasiparticle interactions in frustrated Heisenberg chains
Vanderstraeten, L., Haegeman, J., Verstraete, F., & Poilblanc, D. (2016) · Physical Review B · doi:10.1103/physrevb.93.235108 · Cited by 10
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
- 1388-1398
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W1990885492
- Cited by
- 874
- References
- 13
- FWCI
- 1.15
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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