The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator

TL;DR

This paper derives the Lax connection for a free fermion lattice model from Bazhanov-Stroganov's R-operator, revealing difference-type Yang-Baxter equations suitable for continuum limits of relativistic free fermion theories.

Contribution

It introduces a new derivation of the Lax connection from the fermionic R-operator, connecting lattice models to continuum free fermion theories.

Findings

Derived Lax connection from fermionic R-operator.

Established difference-type Yang-Baxter equations.

Facilitated continuum limit analysis for relativistic free fermions.

Abstract

We derive the Lax connection of the free fermion model on a lattice starting from the fermionic formulation of Bazhanov-Stroganov's three-parameter elliptic parametrization for the R-operator. It results in the Yang-Baxter and decorated Yang-Baxter equations of difference type in one of the spectral parameters, which is the most suitable form to obtain any relativistic model of free fermions in the continuous limit.