The 5-CB Algebra and Fused $SU(2)$ Lattice Models
Abstract
We study the fused 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 BMW (Birman--Murakami--Wenzl) algebra is obeyed by five, six and seven blocks models, conjecturing that it is 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 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.
Keywords
Cite
@article{arxiv.2001.09280,
title = {The 5-CB Algebra and Fused $SU(2)$ Lattice Models},
author = {Vladimir Belavin and Doron Gepner},
journal= {arXiv preprint arXiv:2001.09280},
year = {2021}
}
Comments
20 pages, no figures, Mathematica notebook attached. Added references and corrected some erroneous 5--CB relations