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

2001/08/31 by Klaus Fabricius, Barry M. McCoy
Physics and Astronomy · #cond-mat.stat-mech #hep-th #nlin.SI

paper · pdf

published as MathPhys Odyssey 2001,ed. M.Kashiwara and T.Miwa,Progress in Mathematical Physics, Vol. 23, p.119 · 25 pages,several references added. Several stylistic changes have been made in the interest of clarity

arxiv created 2001/09/18 · arxiv updated 2009/11/30

Abstract

We propose an expression for the current form of the lowering operator of the sl₂ 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.

Related

• Completing Bethe's equations at roots of unity
• Root of unity symmetries in the 8 and 6 vertex models
• XXZ Bethe states as highest weight vectors of the sl₂ loop algebra at roots of unity
• The sl₂ loop algebra symmetry of the six-vertex model at roots of unity
• Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin - [Formula presented] chain