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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/18099We 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.25 pages,several references added. Several stylistic changes have been made in the interest of clarityStatistical MechanicsHigh Energy Physics - TheoryExactly Solvable and Integrable SystemsEvaluation parameters and Bethe roots for the six vertex model at roots of unitytext