Creation operators for the Fateev–Zamolodchikov spin chain

In previous works, we studied the problem of constructing a basis in the space of local operators for an anisotropic XXZ spin chain with spin $1/2$ such that the vacuum expectation values have a simple form. For this, we introduced fermionic creation operators. Here, we extend this construction to the spin-$1$ case. Using a certain version of the fusion procedure, we find two doublets of fermionic creation operators and one triplet of bosonic creation operators. We prove that the basis obtained by the action of these operators satisfies the dual reduced quantum Knizhnik–Zamolodchikov equation.