Elliptic Gaudin models and elliptic KZ Equations

Abstract

The Gaudin models based on the face-type elliptic quantum groups and the $XYZ$ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik-Zamolodchikov equations and their solutions are given.

LaTex file 18 pages; Errors corrected and references added

References in corpus (13)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Gaudin Model, Bethe Ansatz and Critical Level
• Off-Shell Bethe Ansatz Equation and N-point Correlators in the SU(2) WZNW Theory
• Integrable XYZ Spin Chain with Boundaries
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• On representations of the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• Algebraic Bethe Ansatz for XYZ Gaudin model
• Algebraic Bethe ansatz for eight vertex model with general open-boundary conditions
• Generating function of correlators in the sl_2 Gaudin model
• On Integrable Models Related to the $osp(1,2)$ Gaudin Algebra
• Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model
• Bosonization and integral representation of solutions of the Knizhnik-Zamolodchikov-Bernard equations
• Wess-Zumino-Witten model on elliptic curves at the critical level

Cited by in corpus (13)

• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
• Exact solution of the XXZ Gaudin model with generic open boundaries
• Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos
• $A_{n-1}$ Gaudin model with open boundaries
• $Z_n$ elliptic Gaudin model with open boundaries
• 1+1 Gaudin Model
• Decoherence induced by an interacting spin environment in the transition from integrability to chaos
• Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model
• Commuting quantum traces for quadratic algebras
• Gaudin magnet with impurity and its generalized Knizhnik-Zamolodchikov equation
• The Elliptic Gaudin Model: a Numerical Study
• $osp(1|2)$ off-shell Bethe ansatz equation with boundary terms