Bethe Equation of $\tau^{(2)}$-model and Eigenvalues of Finite-size Transfer Matrix of Chiral Potts Model with Alternating Rapidities

TL;DR

This paper derives the Bethe equations for the $ au^{(2)}$-model in the $N$-state chiral Potts model with alternating rapidities and computes transfer matrix eigenvalues using functional relations, highlighting the significance of the alternating superintegrable case.

Contribution

It introduces the Bethe equation for the $ au^{(2)}$-model with alternating rapidities and analyzes eigenvalues of the transfer matrix in this setting, including degeneracy aspects.

Findings

Bethe equations established for the $ au^{(2)}$-model with alternating rapidities.

Eigenvalues of the transfer matrix computed via functional relations.

Degeneracy of $ au^{(2)}$-model discussed in the alternating superintegrable case.

Abstract

We establish the Bethe equation of the $\tau^{(2)}$-model in the $N$-state chiral Potts model (including the degenerate selfdual cases) with alternating vertical rapidities. The eigenvalues of a finite-size transfer matrix of the chiral Potts model are computed by use of functional relations. The significance of the "alternating superintegrable" case of the chiral Potts model is discussed, and the degeneracy of $\tau^{(2)}$-model found as in the homogeneous superintegrable chiral Potts model.