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Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary
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In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial
triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of
anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin
Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in
the periodic case. Once we have the generating function, we obtain the corresponding Gaudin
Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the
generic form of the Bethe vectors such that the off-shell action of the generating function becomes
exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the
generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric
Gaudin model.
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Gaudin model Algebraic bethe ansatz Non-unitary r-matrix
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MDPI