Fusion Operators in the Generalized ${\tau }^{(2)}$-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin

Abstract

We construct the fusion operators in the generalized ${\tau }^{(2)}$-model using the fused $L$-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe ansatz discussion is conducted on two special classes of ${\tau }^{(2)}$ which include the superintegrable chiral Potts model. We then perform the parallel discussion on the XXZ spin chain at roots of unity, and demonstrate that the $s{l}_2$-loop-algebra symmetry exists for the root-of-unity XXZ spin chain with a higher spin, where the evaluation parameters for the symmetry algebra are identified by the explicit Fabricius-McCoy current for the Bethe states. Parallels are also drawn to the comparison with the superintegrable chiral Potts model.

Latex 33 Pages; Typos and errors corrected, New improved version by adding explanations for better presentation. Terminology in the content and the title refined. References added and updated-Journal version

References in corpus (9)

• Transfer matrix functional relations for the generalized tau_2(t_q) model
• Derivation of the order parameter of the chiral Potts model
• Baxter-Bazhanov-Stroganov model: Separation of Variables and Baxter Equation
• The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model
• XXZ Bethe states as highest weight vectors of the $s{l}_2$ loop algebra at roots of unity
• The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
• Solving Baxter's TQ-equation via representation theory
• Root of unity symmetries in the 8 and 6 vertex models
• Chiral Potts Rapidity Curve Descended from Six-vertex Model and Symmetry Group of Rapidities

Cited by in corpus (12)

• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Form-factors in the Baxter-Bazhanov-Stroganov model I: Norms and matrix elements
• Eigenvectors in the Superintegrable Model I: sl_2 Generators
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• Factorized finite-size Ising model spin matrix elements from Separation of Variables
• 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 $U_q(s{l}_2)$
• On ${\tau }^{(2)}$-model in Chiral Potts Model and Cyclic Representation of Quantum Group $U_q(s{l}_2)$
• On $Q$-operators of XXZ Spin Chain of Higher Spin
• Eigenvectors of Baxter-Bazhanov-Stroganov τ^{(2)}(t_q) model with fixed-spin boundary conditions
• 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