Multiple reference states and complete spectrum of the $Z_n$ Belavin model with open boundaries

Abstract

The multiple reference state structure of the ${\mathbb{Z}}_n$ Belavin model with non-diagonal boundary terms is discovered. It is found that there exist $n$ reference states, each of them yields a set of eigenvalues and Bethe Ansatz equations of the transfer matrix. These $n$ sets of eigenvalues together constitute the complete spectrum of the model. In the quasi-classic limit, they give the complete spectrum of the corresponding Gaudin model.

Latex file, 24 pages

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Cited by in corpus (9)

• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Partition function of the eight-vertex model with domain wall boundary condition
• Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end
• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
• Scalar products of the open XYZ chain with non-diagonal boundary terms
• 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