Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary

2017/10/31 by Nicolas Crampe, CNRS-Universit&, #233 +1 · 20 citations
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Bethe ansatz #Black Holes and Theoretical Physics #Boundary (topology) #Chain (unit) #Diagonal #Geometry #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Spin (aerodynamics) #math-ph #math.MP

paper · pdf · doi:10.3842/sigma.2017.094

published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)

arxiv created 2017/12/13 · openalex publication_date 2017/12/13 · arxiv updated 2017/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Diagonalisation d'une classe d'hamiltoniens de spin
• THE QUANTUM METHOD OF THE INVERSE PROBLEM AND THE HEISENBERG XYZ MODEL
• Separation of variables in the open XXX chain
• Boundary conditions for integrable quantum systems
• Algebraic Bethe ansatz for the trigonometric sl(2) Gaudin model with triangular boundary