Evaluation parameters and Bethe roots for the six vertex model at roots of unity

Details Evaluation parameters and Bethe roots for the six vertex model at roots of unity Evaluation parameters and Bethe roots for the six vertex model at roots of unity

2001-08-03

arxiv.org/abs/cond-mat/0108057v3

MathPhys Odyssey 2001,ed. M.Kashiwara and T.Miwa,Progress in Mathematical Physics, Vol. 23, p.119

Physics

Condensed Matter

Statistical Mechanics

25 pages,several references added. Several stylistic changes have been made in the interest of clarity

Scientific paper

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.

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