Lax pair formulation for a small-polaron chain with integrable boundaries

TL;DR

This paper develops a fermionic Lax pair approach to establish the integrability of a small-polaron chain with open boundaries, providing explicit boundary matrices and a direct proof of integrability.

Contribution

It introduces a fermionic Lax pair formulation for the small-polaron model with open boundaries, including explicit boundary supermatrices, confirming its integrability.

Findings

Constructed the Lax pair for the model

Derived boundary supermatrices $K_{\pm}$

Proved the model's integrability

Abstract

Using a fermionic version of the Lax pair formulation, we construct an integrable small-polaron model with general open boundary conditions. The Lax pair and the boundary supermatrices $K_{\pm}$ for the model are obtained. This provides a direct proof of the integrability of the model.