Integrable Boundary Conditions for the One-Dimensional Hubbard Model

TL;DR

This paper explores integrable boundary conditions for the 1D Hubbard model using the Quantum Inverse Scattering Method, identifying diagonal and non-diagonal solutions related to boundary potentials and magnetic fields.

Contribution

It determines the most general integrable boundary conditions for the 1D Hubbard model, including diagonal and non-diagonal solutions via symmetry and covariance properties.

Findings

Identified two diagonal solutions corresponding to boundary chemical potential and magnetic field.

Derived non-diagonal solutions as SO(4) rotations of diagonal solutions.

Established a framework for integrable boundary conditions in fermionic systems.

Abstract

We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted periodic boundary condition and the open boundary condition. We determine the most general form of the integrable twisted periodic boundary condition by considering the symmetry matrix of the fermionic R-matrix. To find the integrable open boundary condition, we shall solve the graded reflection equation, and find there are two diagonal solutions, which correspond to a) the boundary chemical potential and b) the boundary magnetic field. Non-diagonal solutions are obtained using the symmetry matrix of the fermionic R-matrix and the covariance property of the graded reflection equation. They can be interpreted as the SO(4) rotations of the diagonal solutions.