The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity $\eta =\frac{2mK}{N}$ for odd N

Abstract

Following Baxter's method of producing Q_{72}-operator, we construct the Q-operator of the root-of-unity eight-vertex model for the crossing parameter $\eta =\frac{2mK}{N}$ with odd $N$ where Q_{72} does not exist. We use this new Q-operator to study the functional relations in the Fabricius-McCoy comparison between the root-of-unity eight-vertex model and the superintegrable N-state chiral Potts model. By the compatibility of the constructed Q-operator with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we verify the set of functional relations of the root-of-unity eight-vertex model using the explicit form of the Q-operator and fusion weights of SOS model.

arXiv commentLatex 28 page; Typos corrected, minor changes in presentation, References added and updated-Journal version

References in corpus (13)

• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• On representations of the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• Bethe's equation is incomplete for the XXZ model at roots of unity
• Analytic theory of the eight-vertex model
• Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix
• The sl_2 loop algebra symmetry of the six-vertex model at roots of unity
• New Developments in the Eight Vertex Model II. Chains of odd length
• Fusion Operators in the Generalized ${\tau }^{(2)}$-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
• The 8V CSOS model and the $s{l}_2$ loop algebra symmetry of the six-vertex model at roots of unity
• The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
• An elliptic current operator for the 8 vertex model
• Chiral Potts Rapidity Curve Descended from Six-vertex Model and Symmetry Group of Rapidities
• Root of unity symmetries in the 8 and 6 vertex models

Cited by in corpus (8)

• New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
• The TQ equation of the 8 vertex model for complex elliptic roots of unity
• The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of $U_q(s{l}_2)$
• Extended T-systems, Q matrices and T-Q relations for $s\ell (2)$ models at roots of unity
• Elliptic pfaffians and solvable lattice models
• On $Q$-operators of XXZ Spin Chain of Higher Spin
• Bethe Equation of ${\tau }^{(2)}$-model and Eigenvalues of Finite-size Transfer Matrix of Chiral Potts Model with Alternating Rapidities
• Q-operators for higher spin eight vertex models with a rational anisotropy parameter