The 5-CB algebra and fused SU(2) lattice models

We study the fused SU(2) models put forward by Date et al, that are a series of models with arbitrary number of blocks, which is the degree of the polynomial equation obeyed by the Boltzmann weights. We demonstrate by a direct calculation that a version of Birman-Murakami-Wenzl (BMW) algebra [1, 2] is obeyed by five, six and seven blocks models, conjecturing that the BMW algebra is a part of the algebra valid for any model with more than two blocks. To establish this conjecture, we assume that a certain ansatz holds for the baxterization of the models. We use the Yang-Baxter equation to describe explicitly the algebra for five blocks, obtaining 19 additional non-trivial relations. We name this algebra 5-CB (conformal braiding) algebra. Our method can be utilized to describe the algebra for any solvable model of this type and for any number of blocks.

Automated summary

The study examines the fused SU(2) models and their corresponding BMW algebra, demonstrating the satisfaction of the BMW algebra by the five, six, and seven block models, suggesting its applicability to any model with more than two blocks. Using the Yang-Baxter equation, the algebra for the five block model is explicitly described, resulting in 19 additional non-trivial relations.