New symmetries of the chiral Potts model

TL;DR

This paper discovers a new symmetry in the three-state chiral Potts model involving coupled Temperley-Lieb algebras, enabling the construction of superintegrable models and a generalization of the boost-operator.

Contribution

It introduces a previously unknown symmetry involving coupled Temperley-Lieb algebras and develops a generalized boost-operator for generating commuting charges.

Findings

Identification of a new symmetry in the chiral Potts model

Construction of superintegrable models from the symmetry

Development of a generalized boost-operator

Abstract

In this paper a hithertho unknown symmetry of the three-state chiral Potts model is found consisting of two coupled Temperley-Lieb algebras. From these we can construct new superintegrable models. One realisation is in terms of a staggered isotropic XY spin chain. Further we investigate the importance of the algebra for the existence of mutually commuting charges. This leads us to a natural generalisation of the boost-operator, which generates the charges.