Finite-size energy levels of the superintegrable chiral Potts model

TL;DR

This paper derives approximate analytic formulas for the zeros of special polynomials related to the superintegrable chiral Potts model, enabling calculation of finite-size energy corrections without numerical zero determination.

Contribution

It introduces new analytic formulas for polynomial zeros that determine low-lying energy levels in the superintegrable chiral Potts model.

Findings

Analytic expressions for polynomial zeros derived.

Finite-size energy corrections calculated analytically.

Method reduces reliance on numerical zero finding.

Abstract

In the solution of the superintegrable chiral Potts model special polynomials related to the representation theory of the Onsager algebra play a central role. We derive approximate analytic formulae for the zeros of particular polynomials which determine sets of low-lying energy eigenvalues of the chiral Potts quantum chain. These formulae allow the analytic calculation of the leading finite-size corrections to the energy eigenvalues without resorting to a numerical determination of the zeros.