Solutions to the Yang-Baxter equations with $osp_q(1|2)$ symmetry: Lax operators

TL;DR

This paper presents new solutions to the $osp_q(1|2)$-invariant Yang-Baxter equation, including explicit Lax operators and universal R-matrices, advancing the understanding of integrable models with this symmetry.

Contribution

It introduces novel $4\times4$ solutions and explicit $2\times2$ Lax operators for the $osp_q(1|2)$ symmetry, including universal R-matrices and analysis of solutions on fundamental representations.

Findings

Found a new $4\times4$ solution with simple spectral dependence.

Derived universal spectral-parameter dependent R-matrix.

Identified two independent solutions on fundamental three-dimensional representations.

Abstract

We find a new $4\times4$ solution to the $osp_q(1|2)$-invariant Yang-Baxter equation with simple dependence on the spectral parameter and propose $2\times 2$ matrix expressions for the corresponding Lax operator. The general inhomogeneous universal spectral-parameter dependent $R$-matrix is derived. It is proven, that there are two independent solutions to the homogeneous $osp_q(1|2)$-invariant YBE, defined on the fundamental three dimensional representations. One of them is the particular case of the universal matrix, while the second one does not admit generalization to the higher dimensional cases. Also the $3 \times 3$ matrix expression of the Lax operator is found, which have a well defined limit at $q \to 1$.