Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 094, 13 pages      arXiv:1710.08490      https://doi.org/10.3842/SIGMA.2017.094

Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary

Nicolas Crampe
Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, Montpellier, France

Received November 01, 2017, in final form December 06, 2017; Published online December 13, 2017

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.

Key words: integrability; algebraic Bethe ansatz; Gaudin models; Bethe equations.

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