Fermionic R-operator approach for the small-polaron model with open boundary condition

TL;DR

This paper develops a fermionic R-operator approach within the quantum inverse scattering method to establish the integrability and Bethe ansatz solution of the small-polaron model with open boundary conditions.

Contribution

It introduces a novel fermionic R-operator framework that satisfies key integrability equations, providing a new method for analyzing the small-polaron model.

Findings

Proves integrability of the small-polaron model with open boundaries.

Derives Bethe ansatz equations consistent with graded Yang-Baxter formalism.

Establishes dual reflection equations for fermionic operators.

Abstract

Exact integrability and algebraic Bethe ansatz of the small-polaron model with the open boundary condition are discussed in the framework of the quantum inverse scattering method (QISM). We employ a new approach where the fermionic R-operator which consists of fermion operators is a key object. It satisfies the Yang-Baxter equation and the reflection equation with its corresponding K-operator. Two kinds of 'super-transposition' for the fermion operators are defined and the dual reflection equation is obtained. These equations prove the integrability and the Bethe ansatz equation which agrees with the one obtained from the graded Yang-Baxter equation and the graded reflection equations.