Chiral Potts Rapidity Curve Descended from Six-vertex Model and Symmetry Group of Rapidities

Abstract

In this paper, we present a systematical account of the descending procedure from six-vertex model to the $N$-state chiral Potts model through fusion relations of ${\tau }^{(j)}$-operators, following the works of Bazhanov-Stroganov and Baxter-Bazhanov-Perk. A careful analysis of the descending process leads to appearance of the high genus curve as rapidities' constraint for the chiral Potts models. Full symmetries of the rapidity curve are identified, so is its symmetry group structure. By normalized transfer matrices of the chiral Potts model, the ${\tau }^{(2)}T$ relation can be reduced to functional equations over a hyperelliptic curves associated to rapidities, by which the degeneracy of ${\tau }^{(2)}$-eigenvalues is revealed in the case of superintegrable chiral Potts model.

Latex 17 pages ; typos and small errors corrected, references added-Journal version

References in corpus (1)

• Transfer matrix functional relations for the generalized tau_2(t_q) model

Cited by in corpus (6)

• Fusion Operators in the Generalized ${\tau }^{(2)}$-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
• The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
• The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity $\eta =\frac{2mK}{N}$ for odd N
• The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of $U_q(s{l}_2)$
• Bethe Equation of ${\tau }^{(2)}$-model and Eigenvalues of Finite-size Transfer Matrix of Chiral Potts Model with Alternating Rapidities
• The Onsager Algebra Symmetry of ${\tau }^{(j)}$-matrices in the Superintegrable Chiral Potts Model