Completing Bethe's equations at roots of unity

Abstract

In a previous paper we demonstrated that Bethe's equations are not sufficient to specify the eigenvectors of the XXZ model at roots of unity for states where the Hamiltonian has degenerate eigenvalues. We here find the equations which will complete the specification of the eigenvectors in these degenerate cases and present evidence that the $s{l}_2$ loop algebra symmetry is sufficiently powerful to determine that the highest weight of each irreducible representation is given by Bethe's ansatz.

14 pages, Latex. Remarks about the history of BA and Comments about sl_2 loop algebra added. To be published in Journal of Statistical Physics

References in corpus (2)

• Singularities in the Bethe solution of the XXX and XXZ Heisenberg spin chains
• Bases of Bethe Vectors and Difference Equations with Regular Singular Points

Cited by in corpus (5)

• Quantum integrability and supersymmetric vacua
• The six and eight-vertex models revisited
• The six-vertex model at roots of unity and some highest weight representations of the sl(2) loop algebra
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• On the Degenerate Multiplicity of the $s{l}_2$ Loop Algebra for the 6V Transfer Matrix at Roots of Unity