Hubbard Hamiltonian in the dimer representation large-U case

We formulate the Hubbard model for the simple cubic lattice in the representation of interacting dimers applying the exact solution of the dimer problem. This exact solution clearly indicates that doubly occupied lattice sites are present in the case of a large but finite Coulomb repulsion U and are excluded only in the limit U --> infinity. By eliminating from the considerations unoccupied dimer energy levels in the large-U case (it is the only assumption) we analytically derive the Hubbard Hamiltonian of the dimer (analogous to the well-known t - J model), as well as, the complete form of the Hubbard Hamiltonian for the crystal as a whole by means of the projection technique. Using this approach we can better visualize the complexity of the model, so deeply hidden in its original form. The resulting Hamiltonian is a mixture of many multiple ferromagnetic, antiferromagnetic and more exotic interactions competing one with another. The interplay between different competitive interactions has a decisive influence on the resulting thermodynamic properties of the model, depending on temperature, model parameters and assumed average number of electrons per lattice site. A simplified form of the derived Hamiltonian can be obtained using additionally Taylor expansion with respect to x = t/U (t-hopping integral between nearest neighbours). As an example, we present the expansion including all terms proportional to t and to t(2)/U and we reproduce the exact form of the Hubbard Hamiltonian in the limit U --> infinity. The nonperturbative approach, presented in this paper, can, in principle, be applied to clusters of any size, as well as, to another type of model Hamiltonians.