Details
| Original language | English |
|---|---|
| Pages (from-to) | 396-434 |
| Number of pages | 39 |
| Journal | Nuclear Physics, Section B |
| Volume | 336 |
| Issue number | 3 |
| Publication status | Published - 4 Jun 1990 |
| Externally published | Yes |
Abstract
The construction of an integrable generalization of the antiferromagnetic XXZ Heisenberg model with arbitrary spin and easy plane anisotropy is reconsidered. The fusion procedure which has been used to generate models with spin S > 1 2 is shown to give hermitian operators corresponding to the physical conserved quantities only in certain (allowed) regions of the anisotropy γ. The forbidden regions coincide with those where Kirillov and Reshetikhin find restrictions on string locations in a formal Bethe ansatz analysis. In each of the allowed regions for the anisotropy there exists a unique ground-state configuration that does not change with γ. The critical behaviour of the S = 1 and S = 2 spin chains is investigated by numerical solution of their associated Bethe ansatz equations. Our results agree with the known decomposition of the spin model into the semidirect product of a free bosonic (gaussian) and a parafermionic (ZN) theory with N = 2S in the region of small anisotropy (γ < π/2S). They suggest that a similar decomposition holds in certain regions with γ > π/2S. Here, however, N is given by the integer part of π/γ.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Condensed Matter Physics
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematics(all)
- Mathematical Physics
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In: Nuclear Physics, Section B, Vol. 336, No. 3, 04.06.1990, p. 396-434.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The integrable XXZ Heisenberg model with arbitrary spin
T2 - Construction of the Hamiltonian, the ground-state configuration and conformal properties
AU - Frahm, Holger
AU - Yu, Nai Chang
AU - Fowler, Michael
N1 - Funding information: The authors wish to thank H . Johannesson for correspondence on this topic. We also enjoyed interesting discussions with H .J . de Vega . H .F . gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft . Additional support has been provided by the National Science Foundation (NSF) under grant No . DMR-8810541 .
PY - 1990/6/4
Y1 - 1990/6/4
N2 - The construction of an integrable generalization of the antiferromagnetic XXZ Heisenberg model with arbitrary spin and easy plane anisotropy is reconsidered. The fusion procedure which has been used to generate models with spin S > 1 2 is shown to give hermitian operators corresponding to the physical conserved quantities only in certain (allowed) regions of the anisotropy γ. The forbidden regions coincide with those where Kirillov and Reshetikhin find restrictions on string locations in a formal Bethe ansatz analysis. In each of the allowed regions for the anisotropy there exists a unique ground-state configuration that does not change with γ. The critical behaviour of the S = 1 and S = 2 spin chains is investigated by numerical solution of their associated Bethe ansatz equations. Our results agree with the known decomposition of the spin model into the semidirect product of a free bosonic (gaussian) and a parafermionic (ZN) theory with N = 2S in the region of small anisotropy (γ < π/2S). They suggest that a similar decomposition holds in certain regions with γ > π/2S. Here, however, N is given by the integer part of π/γ.
AB - The construction of an integrable generalization of the antiferromagnetic XXZ Heisenberg model with arbitrary spin and easy plane anisotropy is reconsidered. The fusion procedure which has been used to generate models with spin S > 1 2 is shown to give hermitian operators corresponding to the physical conserved quantities only in certain (allowed) regions of the anisotropy γ. The forbidden regions coincide with those where Kirillov and Reshetikhin find restrictions on string locations in a formal Bethe ansatz analysis. In each of the allowed regions for the anisotropy there exists a unique ground-state configuration that does not change with γ. The critical behaviour of the S = 1 and S = 2 spin chains is investigated by numerical solution of their associated Bethe ansatz equations. Our results agree with the known decomposition of the spin model into the semidirect product of a free bosonic (gaussian) and a parafermionic (ZN) theory with N = 2S in the region of small anisotropy (γ < π/2S). They suggest that a similar decomposition holds in certain regions with γ > π/2S. Here, however, N is given by the integer part of π/γ.
U2 - 10.1016/0550-3213(90)90435-G
DO - 10.1016/0550-3213(90)90435-G
M3 - Article
AN - SCOPUS:0007072043
VL - 336
SP - 396
EP - 434
JO - Nuclear Physics, Section B
JF - Nuclear Physics, Section B
SN - 0550-3213
IS - 3
ER -