Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary

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.

References in corpus (7)

• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Separation of Variables in the open XXX chain
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• Determinant representations for scalar products of the XXZ Gaudin model with general boundary terms
• Algebraic Bethe ansatz for the trigonometric sl(2) Gaudin model with triangular boundary

Cited by in corpus (8)

• Heun operator of Lie type and the modified algebraic Bethe ansatz
• Entanglement of Free Fermions on Johnson Graphs
• Bethe ansatz diagonalization of the Heun-Racah operator
• Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz
• Time and band limiting operator and Bethe ansatz
• Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries
• Non-linear integral equations for the XXX spin-1/2 quantum chain with non-diagonal boundary fields
• Exact solution of the Izergin-Korepin Gaudin model with periodic and open boundaries