2 PARTICLES IN THE HUBBARD-MODEL - TOPOLOGY VERSUS PAULI EXCLUSION

We solve the Hubbard model for the case of two particles on an arbitrary Bravais lattice exactly. Although the ground state is almost always a spin singlet, agreeing with the work of Kanamori, for topologically frustrated lattices with positive hopping matrix elements, we find that the ground state is a spin triplet. This topological effect is shown to be rather weak, and does not always survive the jump to finite densities in the thermodynamic limit, where Pauli exclusion strongly stabilises a low spin state. For the two-dimensional triangular lattice and the three-dimensional face-centred cubic lattice, the competition is fiercer and it is not clear whether the ferromagnetism survives.