New Integrable Lattice Models From Fuss-Catalan Algebras

TL;DR

This paper introduces new integrable lattice models derived from Fuss-Catalan algebras, expanding the class of solutions to the Yang-Baxter equation and modeling dense gases of colored loops.

Contribution

It constructs novel trigonometric solutions to the Yang-Baxter equation using Fuss-Catalan algebras, leading to new integrable lattice models.

Findings

New solutions to the Yang-Baxter equation based on Fuss-Catalan algebras.

Development of two-dimensional integrable lattice models for colored loop gases.

Extension of algebraic structures to generate models with multi-colored loop configurations.

Abstract

We construct new trigonometric solutions of the Yang-Baxter equation, using the Fuss-Catalan algebras, a set of multi-colored versions of the Temperley-Lieb algebra, recently introduced by Bisch and Jones. These lead to new two-dimensional integrable lattice models, describing dense gases of colored loops.