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

Abstract

We construct the explicit $Q$-operator incorporated with the $s{l}_2$-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.

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

References in corpus (2)

• Transfer matrix functional relations for the generalized tau_2(t_q) model
• Chiral Potts Rapidity Curve Descended from Six-vertex Model and Symmetry Group of Rapidities

Cited by in corpus (8)

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• The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of $U_q(s{l}_2)$
• On ${\tau }^{(2)}$-model in Chiral Potts Model and Cyclic Representation of Quantum Group $U_q(s{l}_2)$
• Extended T-systems, Q matrices and T-Q relations for $s\ell (2)$ models at roots of unity
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point
• Bethe Equation of ${\tau }^{(2)}$-model and Eigenvalues of Finite-size Transfer Matrix of Chiral Potts Model with Alternating Rapidities
• Duality and Symmetry in Chiral Potts Model