Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions

Abstract

We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe ansatz. It allows us to deal with a generic gl(N) open SNP spin chain possessing on each site an arbitrary representation. As a result, we obtain the Bethe equations in their full generality. The classification of finite dimensional irreducible representations for the twisted Yangians are directly linked to the calculation of the transfer matrix eigenvalues.

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Cited by in corpus (16)

• On the R-matrix realization of Yangians and their representations
• Spectrum and Bethe ansatz equations for the U_ {q}(gl(N)) closed and open spin chains in any representation
• From affine Hecke algebras to boundary symmetries
• The generalized non-linear Schrodinger model on the interval
• Integrable boundary conditions and modified Lax equations
• Nonstandard Bethe Ansatz equations for open O(N) spin chains
• Boundary Lax pairs for the $A_n^{(1)}$ Toda field theories
• Boundary transfer matrices and boundary quantum KZ equations
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• Integrable Models From Twisted Half Loop Algebras
• (Quantum) twisted Yangians: symmetry, Baxterisation and centralizers
• Contracted and expanded integrable structures
• Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry
• Generalized Landau-Lifshitz models on the interval
• Analytical Bethe ansatz in gl(N) spin chains
• The $SU(3)\supset SO(3)$ missing label problem and the analytical Bethe ansatz