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- Construction of the bethe state for the E-tau,E-eta(so(3)) elliptic quantum groupPublication . Manojlovic, Nenad; Nagy, ZoltanElliptic quantum groups can be associated to solutions of the star-triangle relation of statistical mechanics. In this paper, we consider the particular case of the E-tau,E-eta(so(3)) elliptic quantum group. In the context of algebraic Bethe ansatz, we construct the corresponding Bethe creation operator for the transfer matrix defined in an arbitrary representation of E-tau,E-eta(so(3)).
- Algebraic Bethe ansatz for the Sl(2) Gaudin model with boundaryPublication . Cirilo Antonio, N.; Manojlović, Nenad; Ragoucy, E.; Salom, I.Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations. (C) 2015 Published by Elsevier B.V.
- Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin modelPublication . Antonio, N. Cirilo; Manojlović, Nenad; Salom, I.We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model. (C) 2014 The Authors. 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.
- G(2)-Calogero-Moser Lax operators from reductionPublication . Fring, Andreas; Manojlovic, NenadWe construct a Lax operator for the G(2)-Calogero-Moser model by means of a double reduction procedure. In the first reduction step we reduce the A(6)-model to a B-3-model with the help of an embedding of the B-3-root system into the A(6)-root system together with the specification of certain coupling constants. The G(2)-Lax operator is obtained thereafter by means of an additional reduction by exploiting the embedding of the G(2)-system into the B-3-system. The degree of algebraically independent and non-vanishing charges is found to be equal to the degrees of the corresponding Lie algebra.
- 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.