The tetrahedral Zamolodchikov algebra for the fermionic Bazhanov-Stroganov R-operator

TL;DR

This paper introduces a fermionic R-operator derived from Bazhanov-Stroganov's elliptic parametrization, along with related Yang-Baxter equations and a solution to the tetrahedral Zamolodchikov algebra, advancing integrable models in fermionic systems.

Contribution

It presents a novel fermionic R-operator based on elliptic parametrization and solves the tetrahedral Zamolodchikov algebra for a specific case, expanding the understanding of integrable fermionic models.

Findings

Derived fermionic R-operator from elliptic parametrization

Established Yang-Baxter and decorated Yang-Baxter equations of difference type

Provided a solution to the tetrahedral Zamolodchikov algebra for a specific case

Abstract

We find the fermionic R-operator based on Bazhanov-Stroganov three-parameter elliptic parametrization of the free fermion model, and the corresponding Yang-Baxter and decorated Yang-Baxter equations, which are of the difference type in one of the spectral parameters. We also find a solution of the corresponding tetrahedral Zamolodchikov algebra for a specific case.