On $Q$-operators of XXZ Spin Chain of Higher Spin

Abstract

We provide two methods of producing the $Q$-operator of XXZ spin chain of higher spin, one for $N$th root-of-unity $q$ with odd $N$ and another for a general $q$, as the generalization of those known in the six-vertex model. In the root-of-unity case, we discuss the functional relations involving the constructed $Q$-operator for the symmetry study of the theory. The $Q$-operator of XXZ chain of higher spin for a generic $q$ is constructed by extending Baxter's argument in spin-1/2 case for the six-vertex $Q$-operator.

Latex 15 pages

References in corpus (3)

• The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model
• The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity $\eta =\frac{2mK}{N}$ for odd N
• Root of unity symmetries in the 8 and 6 vertex models