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- Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson modelsPublication . Skrypnyk, T.; Manojlović, NenadIn the present paper we develop the algebraic Bethe ansatz approach to the case of non-skew-symmetric gl(2) circle times gl(2)-valued Cartan-non-invariant classical r-matrices with spectral parameters. We consider the two families of these r-matrices, namely, the two non-standard rational r-matrices twisted with the help of second order automorphisms and realize the algebraic Bethe ansatz method for them. We study physically important examples of the Gaudin-type and BCS-type systems associated with these r-matrices and obtain explicitly the Bethe vectors and the spectrum for the corresponding quantum hamiltonians in terms of solutions of Bethe equations. (C) 2021 The Author(s). Published by Elsevier B.V.
- Generalized sℓ(2) Gaudin algebra and corresponding Knizhnik–Zamolodchikov equationPublication . Salom, I.; Manojlović, Nenad; Cirilo António, N.The Gaudin model has been revisited many times, yet some important issues remained open so far. With this paper we aim to properly address its certain aspects, while clarifying, or at least giving a solid ground to some other. Our main contribution is establishing the relation between the off-shell Bethe vectors with the solutions of the corresponding Knizhnik-Zamolodchikov equations for the non-periodic sl(2) Gaudin model, as well as deriving the norm of the eigenvectors of the Gaudin Hamiltonians. Additionally, we provide a closed form expression also for the scalar products of the off-shell Bethe vectors. Finally, we provide explicit closed form of the off-shell Bethe vectors, together with a proof of implementation of the algebraic Bethe ansatz in full generality. (C) 2019 The Authors.
- Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundaryPublication . Salom, I.; Manojlović, NenadWe present a comprehensive treatment of the non-periodic trigonometric s (2) Gaudin model with tri angular boundary, with an emphasis on specific freedom found in the local realization of the generators, as well as in the creation operators used in the algebraic Bethe ansatz. First, we give Bethe vectors of the non-periodic trigonometric s (2) Gaudin model both through a recurrence relation and in a closed form. Next, the off-shell action of the generating function of the trigonometric Gaudin Hamiltonians with gen eral boundary terms on an arbitrary Bethe vector is shown, together with the corresponding proof based on mathematical induction. The action of the Gaudin Hamiltonians is given explicitly. Furthermore, by careful choice of the arbitrary functions appearing in our more general formulation, we additionally obtain: i) the solutions to the Knizhnik-Zamolodchikov equations (each corresponding to one of the Bethe states); ii) compact formulas for the on-shell norms of Bethe states; and iii) closed-form expressions for the off-shell scalar products of Bethe states.
- Rational so(3) Gaudin model with general boundary termsPublication . Manojlović, Nenad; Salom, I.We study the so(3) Gaudin model with general boundary K-matrix in the framework of the algebraic Bethe ansatz. The off-shell action of the generating function of the so(3) Gaudin Hamiltonians is determined. The proof based on the mathematical induction is presented on the algebraic level without any restriction whatsoever on the boundary parameters. The so(3) Gaudin Hamiltonians with general boundary terms are given explicitly as well as their off-shell action on the Bethe states. The correspondence between the Bethe states and the solutions to the generalized so(3) Knizhnik-Zamolodchikov equations is established. In this context, the on-shell norm of the Bethe states is determined as well as their off-shell scalar product.
- Bethe ansatz for the deformed Gaudin modelPublication . Kulish, Petr; Manojlović, Nenad; Samsonov, Maxim; Stolin, AlexanderA deformation of the sl(2) Gaudin model by a Jordanian r-matrix depending on the spectral parameter is constructed. The energy spectrum is preserved and recurrent creation operators are proposed.