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Article

Algebraic Bethe Ansatz for the Trigonometric sℓ(2) Gaudin Model with Triangular Boundary

by 1,† and 2,*,†
1
Departamento de Matemática, F. C. T., Universidade do Algarve, Campus de Gambelas, PT-8005-139 Faro, Portugal
2
Institute of Physics, University of Belgrade, P.O. Box 57, 11080 Belgrade, Serbia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(3), 352; https://doi.org/10.3390/sym12030352
Received: 28 January 2020 / Revised: 18 February 2020 / Accepted: 19 February 2020 / Published: 1 March 2020
(This article belongs to the Special Issue Selected Papers: 10th Mathematical Physics Meeting)
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. View Full-Text
Keywords: Gaudin model; Algebraic Bethe Ansatz; non-unitary r-matrix Gaudin model; Algebraic Bethe Ansatz; non-unitary r-matrix
MDPI and ACS Style

Manojlović, N.; Salom, I. Algebraic Bethe Ansatz for the Trigonometric sℓ(2) Gaudin Model with Triangular Boundary. Symmetry 2020, 12, 352. https://doi.org/10.3390/sym12030352

AMA Style

Manojlović N, Salom I. Algebraic Bethe Ansatz for the Trigonometric sℓ(2) Gaudin Model with Triangular Boundary. Symmetry. 2020; 12(3):352. https://doi.org/10.3390/sym12030352

Chicago/Turabian Style

Manojlović, Nenad, and Igor Salom. 2020. "Algebraic Bethe Ansatz for the Trigonometric sℓ(2) Gaudin Model with Triangular Boundary" Symmetry 12, no. 3: 352. https://doi.org/10.3390/sym12030352

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