$Z_n$ elliptic Gaudin model with open boundaries

Abstract

The $Z_n$ 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 diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

21 pages, Latex file

References in corpus (23)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Pairing in nuclear systems: from neutron stars to finite nuclei
• Spectroscopy of discrete energy levels in ultrasmall metallic grains
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Gaudin Model, Bethe Ansatz and Critical Level
• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Integrability of the pairing hamiltonian
• A Class of Exactly Solvable Pairing Models
• Off-Shell Bethe Ansatz Equation and N-point Correlators in the SU(2) WZNW Theory
• Integrable model for interacting electrons in metallic grains
• Superconducting correlations in metallic nanoparticles: exact solution of the BCS model by the algebraic Bethe ansatz
• Exact solution of the $S{U}_q(n)$ invariant quantum spin chains
• Algebraic Bethe Ansatz for XYZ Gaudin model
• Algebraic Bethe Ansatz for a discrete-state BCS pairing model
• Exact solution of the XXZ Gaudin model with generic open boundaries
• Integrable models for confined fermions: applications to metallic grains
• Solution of the dual reflection equation for $A_{n-1}^{(1)}$ SOS model
• Quasi-classical descendants of disordered vertex models with boundaries
• Exact solution of $Z_n$ Belavin model with open boundary condition
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_n)$ and its applications
• Elliptic Gaudin models and elliptic KZ Equations
• Color superconductivity in cold, dense quark matter

Cited by in corpus (17)

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• Multiple reference states and complete spectrum of the $Z_n$ Belavin model with open boundaries
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• Drinfeld twists of the open XXZ chain with non-diagonal boundary terms
• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
• Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms
• Exact solution of the Izergin-Korepin Gaudin model with periodic and open boundaries