Fermionic R-Operator for the Fermion Chain Model

TL;DR

This paper introduces a new fermionic R-operator within the Quantum Inverse Scattering Method, establishing integrability and deriving conserved quantities for the 1D fermion chain model.

Contribution

It presents a novel fermionic R-operator satisfying a new Yang-Baxter relation, providing a mathematical foundation for integrability and conserved quantities in the fermion chain model.

Findings

New fermionic R-operator satisfying Yang-Baxter relation

Derivation of fermionic Sutherland and Lax equations

Identification of higher conserved quantities using the boost operator

Abstract

The integrability of the one-dimensional (1D) fermion chain model is investigated in the framework of the Quantum Inverse Scattering Method (QISM). We introduce a new R-operator for the fermion chain model, which is expressed in terms of the fermion operators. The R-operator satisfies a new type of the Yang-Baxter relation with fermionic L-operator. We derive the fermionic Sutherland equation from the relation, which is equivalent to the fermionic Lax equation. It also provides a mathematical foundation of the boost operator approach for the fermion model. In fact, we obtain some higher conserved quantities of the fermion model using the boost operator.