Pairing Mechanism in Two Hubbard Models that Show d_(x²-y²) Pairing

Here we examine various aspects of the pairing mechanism for two models, the two-dimensional and two-leg ladder Hubbard models. Both of these models exhibit pairing correlations with d_{x^2-y^2} symmetry. However, the undoped insulating states of these two systems are different with the two-dimensional lattice characterized by a ground state with long-range antiferromagnetic order and the two-leg ladder having a spin gap in its ground state. Our aim is to gain a better understanding of the underlying pairing mechanism which causes d_{x^2-y^2} pairing in these two models.