English

Integrability of the Six-Vertex model and the Yang-Baxter Groupoid

Quantum Algebra 2022-10-27 v1 Mathematical Physics math.MP

Abstract

We study the Yang-Baxter equation for the RR-matrices of the six-vertex model. We analyze the solutions and give new parametrizations of the Yang-Baxter equation. In particular, we find the maximal commutative families of parametrized solutions which generalize the RR-matrices from the affine quantum (super)-groups. Then we give a new parametrization of the Yang-Baxter equation by a groupoid of non-free-fermionic matrices. In the appendix, we study the general algebraic structure of the solutions of the Yang-Baxter and formulate a conjecture that extends the conjecture by Brubaker, Bump, and Friedberg that the composition law on the Yang-Baxter solutions is always associative.

Keywords

Cite

@article{arxiv.2210.14883,
  title  = {Integrability of the Six-Vertex model and the Yang-Baxter Groupoid},
  author = {Slava Naprienko},
  journal= {arXiv preprint arXiv:2210.14883},
  year   = {2022}
}