On the possible existence of an effective momentum-momentum coupling in a correlated electronic system

In this talk, we present a study on how to partly reincorporate the effects of localized binding electrons on the dynamics of their itinerant counterparts in Hubbard-like Hamiltonians. This is done by relaxing the constraint that the former should be entirely frozen in the chemical bonds between the underlying lattice sites through the employment of a Bohr-Oppenheimer ansatz for the wavefunction of the whole electronic system. Accordingly, the latter includes itinerant as well as binding electron coordinates. It is then argued that going beyond the adiabatic approximation, which will be properly justified in due time, we are able to show that the net effect of virtual transitions of binding electrons between their ground and excited states is to furnish the itinerant electrons with an effective inter-electronic momentum-momentum interaction. Once expressed in a localized orbital basis, this term generates new two-body processes which cannot be found even among those neglected in obtaining the Hubbard Hamiltonian. Although we have applied these ideas to the specific case of rings, we are sure they can be easily generalized to higher dimensional systems sharing the required properties of which we have made use herein.