Fermionic lattice models and electronic correlations: Magnetism and superconductivity

We consider the dimer approach to the generalized Hubbard model. As a first step we solve the dimer eigenvalue problem exactly. We decompose the dimer Hamiltonian HD into a set of commuting partial Hamiltonians HD(α)(α=1,2,…,16) ascribed to each dimer energy level where each HD(α) is represented in the second quantization. This procedure gives us a review of important two-site interactions, normally hidden in the original dimer Hamiltonian HD, several of them describing a competition between magnetism and superconductivity but belonging to different dimer energy levels. This feature is, however, a source of new problems discussed in the paper and connected with the practical use of the mean field approximation in the case of a real lattice. As a next step, we consider the decomposition of the real lattice into a set of interacting dimers to explicitly show that the competition between magnetism and superconductivity is a common feature of all electronic lattice models. This competition should be necessarily taken into account in practical calculations of the thermodynamics of such models.