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Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions

Quantum Algebra 2024-11-21 v2 Statistical Mechanics High Energy Physics - Theory Mathematical Physics math.MP Exactly Solvable and Integrable Systems

Abstract

We find all solutions to the constant Yang--Baxter equation R12R13R23=R23R13R12R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12} in three dimensions, subject to an additive charge-conservation ansatz. This ansatz is a generalisation of (strict) charge-conservation, for which a complete classification in all dimensions was recently obtained. Additive charge-conservation introduces additional sector-coupling parameters -- in 3 dimensions there are 44 such parameters. In the generic dimension 3 case, in which all of the 44 parameters are nonzero, we find there is a single 3 parameter family of solutions. We give a complete analysis of this solution, giving the structure of the centraliser (symmetry) algebra in all orders. We also solve the remaining cases with three, two, or one nonzero sector-coupling parameter(s).

Keywords

Cite

@article{arxiv.2310.03816,
  title  = {Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions},
  author = {Jarmo Hietarinta and Paul Martin and Eric C. Rowell},
  journal= {arXiv preprint arXiv:2310.03816},
  year   = {2024}
}

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