Bethe Ansatz and Symmetry in Superintegrable Chiral Potts Model and Root-of-unity Six-vertex Model

TL;DR

This paper explores the symmetry structures of the superintegrable chiral Potts model and the root-of-unity six-vertex model, revealing their algebraic relations via Bethe ansatz and functional equations.

Contribution

It provides a unified analysis of the Onsager algebra and $sl_2$-loop algebra symmetries in these models using $Q$-operators and fusion matrices.

Findings

Identifies the algebraic symmetry correspondence between the models.

Develops a uniform Bethe ansatz framework for both models.

Clarifies the role of functional relations in symmetry analysis.

Abstract

We examine the Onsager algebra symmetry of $\tau^{(j)}$-matrices in the superintegrable chiral Potts model. The comparison of Onsager algebra symmetry of the chiral Potts model with the $sl_2$-loop algebra symmetry of six-vertex model at roots of unity is made from the aspect of functional relations using the $Q$-operator and fusion matrices. The discussion of Bethe ansatz for both models is conducted in a uniform manner through the evaluation parameters of their symmetry algebras.