R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz

Abstract

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 arXiv:1306.6303, on three state $U(1)$-invariant Hamiltonians solvable by CBA, 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 arXiv:1303.4010, 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.

arXiv comment22 pages

References in corpus (6)

• Bethe Ansatze for 19-vertex Models
• Symmetries of spin systems and Birman-Wenzl-Murakami algebra
• Exact solution of new integrable nineteen-vertex models and quantum spin-1 chains
• Classification of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
• Integrable three-state vertex models with weights lying on genus five curves
• Phase diagram and spectral properties of a new exactly integrable spin one quantum chain

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