Nested algebraic Bethe ansatz for open GL(N) spin chains with projected K-matrices

Abstract

We consider an open spin chain model with GL(N) bulk symmetry that is broken to GL(M) x GL(N-M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing the corresponding commuting transfer matrix. This construction uses operator-valued "projected" K-matrices. We solve this model for general values of N and M using the nested algebraic Bethe ansatz approach, despite the fact that the K-matrices are not diagonal. The key to obtaining this solution is an identity based on a certain factorization property of the reduced K-matrices into products of R-matrices. Numerical evidence suggests that the solution is complete.

27 pages; v2: minor change; v3: references added

References in corpus (16)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach
• Conformal boundary loop models
• The two-boundary Temperley-Lieb algebra
• Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
• Exact solutions and elementary excitations in the XXZ spin chain with unparallel boundary fields
• Conformal boundary conditions in the critical O(n) model and dilute loop models
• Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
• Combinatorial aspects of boundary loop models
• The Bethe Ansatz Equations for Reflecting Magnons
• A note on the boundary spin $s$ XXZ chain
• Bethe ansatz equations for open spin chains from giant gravitons
• Boundary operators in the O(n) and RSOS matrix models
• Boundary transitions of the O(n) model on a dynamical lattice
• Boundary changing operators in the O(n) matrix model

Cited by in corpus (5)

• Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
• On Separation of Variables for Reflection Algebras
• Revisiting the Y=0 open spin chain at one loop
• Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
• The dilatation operator for defect conformal N=4 SYM