Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices

Abstract

We consider a formulation of the algebraic Bethe ansatz for the six vertex model with non-diagonal open boundaries. Specifically, we study the case where both left and right $K$-matrices have an upper triangular form. We show that the main difficulty entailed by those form of the $K$-matrices is the construction of the excited states. However, it is possible to treat this problem with aid of an auxiliary transfer matrix and by means of a generalized creation operator.

arXiv commentv2: Minor changes. Published version. 19 pages

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• 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
• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
• Correlation functions of the half-infinite XXZ spin chain with a triangular boundary
• Integrable dissipative exclusion process: Correlation functions and physical properties
• Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries
• Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary
• Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment
• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
• Form factors of the half-infinite XXZ spin chain with a triangular boundary
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Scalar product for the XXZ spin chain with general integrable boundaries
• Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices
• Bethe States of the integrable spin-s chain with generic open boundaries