R matrices of three-state Hamiltonians solvable by coordinate Bethe ansatz

We review some of the strategies that can be implemented to infer an R-matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in Crampé, Frappat, and Ragoucy, J. Phys. A 46, 405001 (2013), on three state U(1)-invariant Hamiltonians solvable by coordinate Bethe ans...

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Bibliographic Details
Published in:Journal of mathematical physics 2015-01, Vol.56 (1), p.1
Main Authors: Fonseca, T, Frappat, L, Ragoucy, E
Format: Article
Language:English
Subjects:
Classification
Knowledge
Mathematical Physics
Matrix
Physics
Theorems
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Summary:We review some of the strategies that can be implemented to infer an R-matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in Crampé, Frappat, and Ragoucy, J. Phys. A 46, 405001 (2013), on three state U(1)-invariant Hamiltonians solvable by coordinate Bethe ansatz, focusing on models for which the S-matrix is not trivial. For the 19-vertex solutions, we recover the R-matrices of the well-known Zamolodchikov–Fateev and Izergin–Korepin models. We point out that the generalized Bariev Hamiltonian is related to both main and special branches studied by Martins in Nucl. Phys. B 874, 243 (2013), that we prove to generate the same Hamiltonian. The 19-vertex SpR model still resists to the analysis, although we are able to state some no-go theorems on its R-matrix. For 17-vertex Hamiltonians, we produce a new R-matrix.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4905893