On extension of the Yang-Baxter equation and the fermionic $R$-operator

TL;DR

This paper extends the Yang-Baxter equation by constructing a more general fermionic R-operator based on elliptic parametrization, solving related algebraic structures, and deriving an extended difference-type Yang-Baxter equation.

Contribution

It introduces a generalized fermionic R-operator and extends the Yang-Baxter equation using elliptic parametrization and solutions to the tetrahedral Zamolodchikov algebra.

Findings

Derived the most general solution of the tetrahedral Zamolodchikov algebra in the trigonometric limit.

Constructed an extended R-operator and Yang-Baxter equation of difference type.

Provided a framework for further exploration of integrable models with fermionic R-operators.

Abstract

We consider the fermionic $R$-operator based on Bazhanov-Stroganov's three-parameter elliptic parametrization of the free fermion model, and find the most general solution of the related tetrahedral Zamolodchikov algebra in the trigonometric limit for an arbitrary set of parameters. This allows to construct an extension of the $R$-operator and the corresponding Yang-Baxter equation, which are of the difference type in one of the spectral parameters.