Boundary two-parameter eight-state supersymmetric fermion model and Bethe ansatz solution

TL;DR

This paper extends a supersymmetric fermion model to include boundary conditions, demonstrating its integrability and solving it using the Bethe ansatz for nine different boundary classes.

Contribution

It introduces boundary terms to a supersymmetric fermion model, constructs nine integrable boundary conditions, and provides their Bethe ansatz solutions.

Findings

Nine classes of boundary conditions are integrable.

Bethe ansatz equations are derived for all boundary cases.

The model's integrability is confirmed via the graded boundary quantum inverse scattering method.

Abstract

The recently introduced two-parameter eight-state $U_q[gl(3|1)]$ supersymmetric fermion model is extended to include boundary terms. Nine classes of boundary conditions are constructed, all of which are shown to be integrable via the graded boundary quantum inverse scattering method. The boundary systems are solved by using the coordinate Bethe ansatz and the Bethe ansatz equations are given for all nine cases.