Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary

TL;DR

This paper develops a modified algebraic Bethe ansatz approach to solve the XXZ Gaudin model with generic boundary conditions, covering various cases including higher spins, and deriving the corresponding Bethe equations.

Contribution

It introduces a unified method to solve the XXZ Gaudin model with generic boundary, extending previous results to include higher spins and inhomogeneous Bethe equations.

Findings

Derived Bethe equations for all boundary cases

Unified treatment of diagonal, triangular, and generic boundaries

Extended solutions to higher spin Gaudin models

Abstract

We solve the XXZ Gaudin model with generic boundary using the modified algebraic Bethe ansatz. The diagonal and triangular cases have been recovered in this general framework. We show that the model for odd or even lengths has two different behaviors. The corresponding Bethe equations are computed for all the cases. For the chain with even length, inhomogeneous Bethe equations are necessary. The higher spin Gaudin models with generic boundary is also treated.