The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
Abstract
We construct the explicit -operator incorporated with the -loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the -operator, the six-vertex transfer matrix and fusion matrices are derived from the Bethe equation, parallel to the Onsager-algebra-symmetry discussion in the superintegrable -state chiral Potts model. We show that the whole set of functional equations is valid for the -operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the -operator in the symmetry study of root-of-unity six-vertex model from the functional-relation aspect.
Cite
@article{arxiv.cond-mat/0602375,
title = {The Q-operator for Root-of-Unity Symmetry in Six Vertex Model},
author = {Shi-shyr Roan},
journal= {arXiv preprint arXiv:cond-mat/0602375},
year = {2010}
}
Comments
Latex 26 Pages; Typos and small errors corrected, Some explanations added for clearer presentation, References updated-Journal version with modified labelling of sections and formulas