Completing Bethe's equations at roots of unity

2000/12/31 by Klaus Fabricius, Barry M. McCoy
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #hep-th #math-ph #math.MP #math.QA #math.RT

paper · pdf

published as J.Statist.Phys. 104 (2001) 573-587 · 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

arxiv created 2001/03/29 · arxiv updated 2009/11/30

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 sl₂ loop algebra symmetry is sufficiently powerful to determine that the highest weight of each irreducible representation is given by Bethe's ansatz.

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