A conjecture for the superintegrable chiral Potts model

TL;DR

This paper proposes a conjecture for calculating matrix elements related to the superintegrable chiral Potts model's magnetization, aiming to enable algebraic derivations akin to the Ising model.

Contribution

It introduces a conjecture expressing key matrix elements as determinants, extending previous results to facilitate algebraic analysis of the model.

Findings

Conjectured determinant formula for matrix elements of e^{-eta H} S^r_1 e^{-eta H}

Expression of spontaneous magnetization in terms of these matrix elements

Potential for algebraic derivation of magnetization similar to Yang's approach for the Ising model

Abstract

We adapt our previous results for the ``partition function'' of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{-\alpha H}, where H is the associated hamiltonian. The spontaneous magnetization M_r can be expressed in terms of particular matrix elements of e^{-\alpha H} S^r_1 \e^{-\beta H}, where S_1 is a diagonal matrix.We present a conjecture for these matrix elements as an m by m determinant, where m is proportional to the width of the lattice. The author has previously derived the spontaneous magnetization of the chiral Potts model by analytic means, but hopes that this work will facilitate a more algebraic derivation, similar to that of Yang for the Ising model.