标题： 三态哈密顿量的R矩阵，可通过坐标贝特方法求解 显示英文标题

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

摘要： 我们回顾了一些可以实施的策略，以从其哈密顿量的知识中推断出一个$R$矩阵。 我们将它们应用于 arXiv:1306.6303 中实现的分类，针对三个状态$U(1)$不变的可由CBA求解的哈密顿量，重点关注$S$矩阵不平凡的模型。 对于19顶点解，我们恢复了著名的 Zamolodchikov--Fateev 和 Izergin--Korepin 模型的$R$矩阵。 我们指出，广义的 Bariev 哈密顿量与 Martins 在 arXiv:1303.4010 中研究的主要分支和特殊分支有关，我们证明它们生成相同的哈密顿量。 19顶点 SpR 模型仍然难以分析，尽管我们能够对其$R$矩阵提出一些无解定理。 对于17顶点哈密顿量，我们产生了一个新的$R$矩阵。 显示英文摘要

摘要： 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.