R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
arXiv:1406.3197 · doi:10.1063/1.4905893
Abstract
We review some of the strategies that can be implemented to infer an -matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in arXiv:1306.6303, on three state -invariant Hamiltonians solvable by CBA, focusing on models for which the -matrix is not trivial. For the 19-vertex solutions, we recover the -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 -matrix. For 17-vertex Hamiltonians, we produce a new -matrix.
22 pages