The integrable XXZ Heisenberg model with arbitrary spin

Construction of the Hamiltonian, the ground-state configuration and conformal properties

authored by: Holger Frahm, Nai Chang Yu, Michael Fowler
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 (Z_N) 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.
External Organisation(s): University of Virginia
Type: Article
Journal: Nuclear Physics, Section B
Volume: 336
Pages: 396-434
No. of pages: 39
ISSN: 0550-3213
Publication date: 04.06.1990
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Condensed Matter Physics, Nuclear and High Energy Physics, Mathematical Physics
Electronic version(s): https://doi.org/10.1016/0550-3213(90)90435-G (Access: Unknown)

BibTeX

@article{088386b94e134b44af53bb5d4500e0ce,
title = "The integrable XXZ Heisenberg model with arbitrary spin: Construction of the Hamiltonian, the ground-state configuration and conformal properties",
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.",
author = "Holger Frahm and Yu, {Nai Chang} and Michael Fowler",
note = "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 .",
year = "1990",
month = jun,
day = "4",
doi = "10.1016/0550-3213(90)90435-G",
language = "English",
volume = "336",
pages = "396--434",
journal = "Nuclear Physics, Section B",
issn = "0550-3213",
publisher = "Elsevier",
number = "3",
}