New symmetries of the chiral Potts model

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.

19 pages, improved notation, made the text easier to read, corrected some typos

References in corpus (2)

• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• Corner transfer matrices in statistical mechanics

Cited by in corpus (4)

• Onsager algebra and algebraic generalization of Jordan-Wigner transformation
• Pivoting through the chiral-clock family
• A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain
• The planar parafermion algebra: The ${\mathbb{Z}}_N$ clock model and the coupled Temperley-Lieb algebra