The Q-operator for Root-of-Unity Symmetry in Six Vertex Model

Details The Q-operator for Root-of-Unity Symmetry in Six Vertex Model The Q-operator for Root-of-Unity Symmetry in Six Vertex Model

2006-02-16

arxiv.org/abs/cond-mat/0602375v3

J.Phys.A39:12303-12326,2006

Physics

Condensed Matter

Statistical Mechanics

Latex 26 Pages; Typos and small errors corrected, Some explanations added for clearer presentation, References updated-Journal

Scientific paper

10.1088/0305-4470/39/40/002

We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-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 $N$-state chiral Potts model. We show that the whole set of functional equations is valid for the $Q$-operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the $Q$-operator in the symmetry study of root-of-unity six-vertex model from the functional-relation aspect.

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