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.

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• Equivalent T-Q relations and exact results for the open TASEP
• Bethe ansatz diagonalization of the Heun-Racah operator
• Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz
• Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries
• Time and band limiting operator and Bethe ansatz
• "Bethe-Ansatz-free" eigenstates of spin-1/2 Richardson-Gaudin integrable models
• 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