Bethe Equations for a g_2 Model

TL;DR

This paper proves the exact solvability of a three-particle g_2 model using the coordinate Bethe ansatz, deriving Bethe equations through Weyl group properties and a generalized Yang-Baxter equation.

Contribution

It introduces a novel application of the coordinate Bethe ansatz to a g_2 model and derives Bethe equations using a generalized Yang-Baxter equation.

Findings

Exact solvability of the g_2 model established

Bethe equations derived from Weyl group properties

Identification of non-trivial solutions to the generalized Yang-Baxter equation

Abstract

We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the properties of the Weyl group, we are also able to find Bethe equations. It is notable that the method relies on a certain generalized version of the well-known Yang-Baxter equation. A particular class of non-trivial solutions to this equation emerges naturally.