Fusion of Dilute $A_L$ Lattice Models

TL;DR

This paper develops a fusion hierarchy and Bethe ansatz equations for dilute $A_L$ lattice models, revealing an $su(3)$ structure, and sets the stage for solving their eigenvalue spectra.

Contribution

It introduces a fusion hierarchy with an $su(3)$ structure and derives Bethe ansatz equations for dilute $A_L$ models, advancing their analytical understanding.

Findings

Fusion hierarchy of functional equations with $su(3)$ structure

Bethe ansatz equations for dilute $A_L$ models

Connection between fusion hierarchy and eigenvalue spectra

Abstract

The fusion procedure is implemented for the dilute $A_L$ lattice models and a fusion hierarchy of functional equations with an $su(3)$ structure is derived for the fused transfer matrices. We also present the Bethe ansatz equations for the dilute $A_L$ lattice models and discuss their connection with the fusion hierarchy. The solution of the fusion hierarchy for the eigenvalue spectra of the dilute $A_L$ lattice models will be presented in a subsequent paper.