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arXiv:cond-mat/0411419 · To appear in the proceedings of

Root of unity symmetries in the 8 and 6 vertex models

K. Fabricius, Barry M. McCoy

Published Nov 16, 2004• 6 citations
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Abstract

We review the recently discovered symmetries of the 8 and 6 vertex models which exist at roots of unity and present their relation with representation theory of affine Lie algebras, Drinfeld polynomials and Bethe vectors.
DOI
10.48550/arxiv.cond-mat/0411419

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We propose an expression for the current form of the lowering operator of the sl 2 loop algebra symmetry of the six-vertex model (XXZ spin chain) at roots of unity. This operator has poles which correspond to the evaluation parameters of representation theory which are given as the roots of the Drinfeld polynomial. We explicitly compute these polynomials in terms of the Bethe roots which characterize the highest weight states for all values of S z . From these polynomials we find that the Bethe roots satisfy sum rules for each value of S z .