Integrable open-boundary conditions for the $q$-deformed supersymmetric $U$ model of strongly correlated electrons

TL;DR

This paper develops a boundary quantum inverse scattering framework for integrable models and applies it to the q-deformed supersymmetric U model, deriving boundary conditions and Bethe ansatz solutions.

Contribution

It introduces a general graded reflection algebra and formulates a boundary quantum inverse scattering method applicable to boundary lattice systems.

Findings

Derived diagonal boundary K-matrices for the model

Identified integrable boundary terms for the system

Solved the boundary system using coordinate Bethe ansatz

Abstract

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the $q$-deformed supersymmetric $U$ model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property.