W = 0 pairing in Hubbard and related models of low-dimensional superconductors

Abstract

Lattice Hamiltonians with on-site interactionW have W = 0 solutions, that is, many-body singlet eigenstates without double occupation. In particular,W = 0 pairs give a clue to understand the pairing force in repulsive Hubbard models. Theseeigenstates are found in systems with high enough symmetry, like the square, hexagonal ortriangular lattices. By a general theorem, we propose a systematic way to construct all theW = 0 pairs of a given Hamiltonian. We also introduce a canonical transformation to calculate theeffective interaction between the particles of such pairs. In geometries appropriate for theCuO2 planes of cuprate superconductors, armchair carbon nanotubes, or cobalt oxide planes, the dressedpair becomes a bound state in a physically relevant range of parameters. We also show thatW = 0 pairs quantize the magnetic flux as superconducting pairs do. The pairingmechanism breaks down in the presence of strong distortions. TheW = 0 pairs are also the building blocks for the antiferromagnetic ground state of thehalf-filled Hubbard model at weak coupling. Our analytical results for the4 × 4 Hubbard square lattice, compared to available numerical data, demonstrate that the method,besides providing an intuitive grasp on pairing, also has quantitative predictive power. We alsoconsider including phonon effects in this scenario. Preliminary calculations with small clustersindicate that vector phonons hinder pairing while half-breathing modes are synergic with theW = 0 pairing mechanism both at weak coupling and in the polaronic regime.