Exact solution of a quantum integrable system associated with the $G_2$ exceptional Lie algebra

TL;DR

This paper derives the exact energy spectrum and Bethe ansatz equations for a quantum integrable spin chain linked to the exceptional Lie algebra G_2, using fusion techniques and polynomial analysis.

Contribution

It introduces a unified method to solve Bethe ansatz equations for systems related to exceptional Lie algebras with various boundary conditions.

Findings

Exact energy spectrum derived

Bethe ansatz equations formulated

Unified approach for boundary conditions

Abstract

A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to derive the exact energy spectrum and Bethe ansatz equations of the system based on polynomial analysis. The present method provides a unified treatment to investigate the Bethe ansatz solutions for both periodic and non-diagonal open boundary conditions associated with exceptional Lie algebras.