On the Hubbard model with boundaries

Hitoshi Asakawa, Masuo Suzuki

Elementary excitations in the one-dimensional Hubbard model with boundary fields are discussed. Boundary scattering matrices for the excitations of the charge and spin sectors are evaluated. Both the repulsive and the attractive Hubbard models at half-filling and without a magnetic field are studied.

Alain Messager, Сергей Анатольевич Пирогов, Yuri Suhov

Élliott H. Lieb

Jiang Yi

Quantum impurity models have deep connection with the boundary problem.Low-dimensional materials have been an additional source of motivation to investigate onedimensional exactly solvable models.We will study the common Hubbard model,and then study the Hubbard model with open boundary conditions.

Xu Yuan, Xin-Zhong Yan

The Cooper pairing near the boundary of a superconductor is analyzed by using the linear-response theory. The system is described by the square lattice ( t , - U ) Hubbard model occupying half space. At half filling, the pairing also corresponds to the antiferromagnetic ordering in the repulsive Hubbard model. The numerical result clearly shows that, at weak to intermediate coupling ( U / t ⩽ 1), the boundary exerts strong influence on the order parameter; the weaker the coupling, the deeper the order parameter is suppressed near the boundary. The present scheme is valid in the whole temperature regime of Cooper pairing.

Élliott H. Lieb