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 $sl_2$ loop algebra symmetry is sufficiently powerful to determine that the highest weight of each irreducible representation is given by Bethe's ansatz.
 Publication:

arXiv eprints
 Pub Date:
 December 2000
 arXiv:
 arXiv:condmat/0012501
 Bibcode:
 2000cond.mat.12501F
 Keywords:

 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 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