Integrable Hamiltonians with $D(D_n)$ symmetry from the Fateev-Zamolodchikov model

TL;DR

This paper constructs integrable Hamiltonians with dihedral group symmetry from a special Fateev-Zamolodchikov model solution, enabling the derivation of functional relations and Bethe ansatz equations.

Contribution

It introduces a new integrable model with D(D_n) symmetry derived from the Fateev-Zamolodchikov model, expanding the understanding of symmetries in integrable systems.

Findings

Derived a solution to the Yang-Baxter equation with two spectral parameters.

Established the symmetry of the resulting models as the Drinfeld double of a dihedral group.

Constructed functional relations and Bethe ansatz equations for the model.

Abstract

A special case of the Fateev-Zamolodchikov model is studied resulting in a solution of the Yang-Baxter equation with two spectral parameters. Integrable models from this solution are shown to have the symmetry of the Drinfeld double of a dihedral group. Viewing this solution as a descendant of the zero-field six-vertex model allows for the construction of functional relations and Bethe ansatz equations.