Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org