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

T. Fonseca , L. Frappat (1) , E. Ragoucy (1)

1 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

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 Crampe, 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

Domaines: Physique mathématique [math-ph]

T. Fonseca, L. Frappat, E. Ragoucy. R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz. Journal of Mathematical Physics, 2015, 56 (1), pp.013503. ⟨10.1063/1.4905893⟩. ⟨hal-01168975⟩