Elliptic Gaudin models and elliptic KZ equations

  title={Elliptic Gaudin models and elliptic KZ equations},
  author={Mark D.Gould and Yao-Z Zhang and Shaoyou Zhao},
  journal={Nuclear Physics},
Z(n) elliptic Gaudin model with open boundaries
The n elliptic Gaudin model with integrable boundaries specified by generic non-diagonal K-matrices with n+1 free boundary parameters is studied. The commuting families of Gaudin operators are
The dynamical elliptic quantum Gaudin models and their solutions
In this paper, we construct the Hamiltonians of both periodic and open elliptic quantum Gaudin models and show their relations with the elliptic quantum group, and the boundary elliptic quantum
Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model ?
In this paper we construct the quantum spectral curve for the quantum dynami- cal elliptic gl n Gaudin model. We realize it considering a commutative family corresponding to the Felder's elliptic
The Elliptic Gaudin Model: a Numerical Study
The elliptic Gaudin model describes completely anisotropic spin systems with long range interactions. The model was proven to be quantum integrable by Gaudin and latter the exact solution was found
$A_{n-1}$ Gaudin model with generic open boundaries
The An−1 Gaudin model with generic integerable boundaries specified by nondiagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz
+1 Gaudin Model
We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For sl(N) case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic
osp(1|2) off-shell Bethe ansatz equation with boundary terms
This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the osp(1|2) vertex model with diagonal K matrices. In this limit Gaudin’s Hamiltonians


Wess-Zumino-Witten model on elliptic curves at the critical level.
We construct a Gaudin-type lattice model as the Wess-Zumino-Witten model on elliptic curves at the critical level. Bethe eigenvectors are obtained by the bosonization technique.
Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model
Using quasiclassical limit of Baxter's 8 - vertex R - matrix, an elliptic generalization of the Knizhnik-Zamolodchikov equation is constructed. Via Off-Shell Bethe ansatz an integrable representation
Gaudin model, Bethe Ansatz and critical level
We propose a new method of diagonalization oif hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on the Wakimoto modules over affine algebras at the
On Integrable Models Related to the osp(1, 2) Gaudin Algebra
The osp(1,2) Gaudin algebra is defined and integrable models described by it are considered. The models include the osp(1,2) Gaudin magnet and the Dicke model related to it. Detailed discussion of
Gaudin magnet with boundary and generalized Knizhnik-Zamolodchikov equation
We consider the boundary quantum inverse scattering method established by Sklyanin (1988). The Gaudin magnet with boundary is diagonalized by taking a quasi-classical limit of the inhomogeneous
Separation of variables in the Gaudin model
We separate variables for the Gaudin model (degenerate case of an integrable quantum magnet SU(2) -chain) by means of an explicit change of coordinates. We get a description of the space of states in
Generating Function of Correlators in the sl2 Gaudin Model
An exponential generating function of correlators is calculated explicitly for the sl2 Gaudin model (degenerated quantum integrable XXX spin chain). The calculation relies on the Gauss decomposition
Bosonization and Integral Representation of Solutions¶of the Knizhnik–Zamolodchikov–Bernard Equations
Abstract:We construct an integral representation of solutions of the Knizhnik–Zamolodchikov–Bernard equations, using the Wakimoto modules.