# Algebraic Bethe ansatz for the XYZ Gaudin model

@article{Sklyanin1996AlgebraicBA, title={Algebraic Bethe ansatz for the XYZ Gaudin model}, author={E. K. Sklyanin and Takashi Takebe}, journal={Physics Letters A}, year={1996}, volume={219}, pages={217-225} }

Abstract The eigenvectors of the Hamiltonians of the XYZ Gaudin model are constructed by means of the algebraic Bethe ansatz. The construction is based on the quasiclassical limit of the corresponding results for the inhomogeneous higher spin eight vertex model.

## 47 Citations

Exact solution of the XXZ Gaudin model with generic open boundaries

- Physics, Mathematics
- 2004

The XXZ Gaudin model with generic integrable boundaries specified by generic non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe…

An−1 Gaudin model with open boundaries

- Physics
- 2005

Abstract The A n − 1 Gaudin model with integrable boundaries specified by non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz…

Algebraic Bethe ansatz for the sℓ(2) Gaudin model with boundary

- Physics, Mathematics
- 2015

Abstract 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…

Direct Proof of Determinant Representation for Scalar Products of the XXZ Gaudin Model with Generic Non-Diagonal Boundary Terms ⁄

- Mathematics
- 2014

After constructing the Bethe state of the XXZ Gaudin model with generic non-diagonal boundary terms, we analyze the properties of this state and obtain the determinant representations of the scalar…

Exact solution of the XXX Gaudin model with generic open boundaries

- Physics, Mathematics
- 2015

Abstract The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated…

Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

- Physics, Mathematics
- 2014

Abstract 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…

Separation of Variables in the Elliptic Gaudin Model

- Mathematics, Physics
- 1999

Abstract:For the elliptic Gaudin model (a degenerate case of the XYZ integrable spin chain) a separation of variables is constructed in the classical case. The corresponding separated coordinates are…

The new formulas for the eigenvectors of the Gaudin model in the so(5) case

- Physics
- 2011

In our recent paper we proposed new formulas for eigenvectors of the Gaudin model in sl(3) case. Similarly in this paper we used the standard Bethe Ansatz method for finding the eigenvectors and the…

Generalized SUq(1|2) Gaudin model

- Mathematics
- 2001

In this paper we propose the Hamiltonians of the generalized SUq(1|2) Gaudin model corresponding to the periodic generalized t-J model. With the help of the well defined graded quantum determinant,…

Algebraic Bethe ansatz for deformed Gaudin model

- Mathematics, Physics
- 2011

The Gaudin model based on the sl2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of…

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