At roots of unity the $N$ -state integrable chiral Potts model and the six-vertex model descend from each other with the $τ_2$ model as the intermediate. We shall discuss how different gauge choices in the six-vertex model lead to two different quantum group constructions with different $q$ -Pochhammer symbols, one construction only working well for $N$ odd, the other equally well for all $N$ . We also address the generalization based on the sl $(m,n)$ vertex model.At roots of unity the $N$-state integrable chiral Potts model and the six-vertex model descend from each other with the $τ_2$ model as the intermediate. We shall discuss how different gauge choices in the six-vertex model lead to two different quantum group constructions with different $q$-Pochhammer symbols, one construction only working well for $N$ odd, the other equally well for all $N$. We also address the generalization based on the sl$(m,n)$ vertex model.

arXiv:1806.03359Jun 8, 20180 citations

Quasi-classical descendants of disordered vertex models with boundaries

Antonio Di Lorenzo, Luigi Amico A, Kazuhiro Hikami +2 more

arXiv:cond-mat/0206521Nuclear Physics BNov 1, 200230 citations

CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra

Helen Au-Yang, Jacques H. H. Perk

Abstract Monodromy matrices of the model are known to satisfy a Yang–Baxter equation with a six-vertex R -matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R -matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.Abstract Monodromy matrices of the model are known to satisfy a Yang–Baxter equation with a six-vertex R -matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R -matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.

arXiv:1511.08523Journal of Physics A Mathematical and TheoreticalMar 8, 20164 citations

At roots of unity the

N

-state integrable chiral Potts model and the six-vertex model descend from each other with the

τ_2

model as the intermediate. We shall discuss how different gauge choices in the six-vertex model lead to two different quantum group constructions with different

q

-Pochhammer symbols, one construction only working well for

N

odd, the other equally well for all

N

. We also address the generalization based on the sl

(m,n)

vertex model.