NUMERICAL METHODS FOR STRONGLY CORRELATED ELECTRONS IN ONE DIMENSIONAL FINITE SIX SITES SYSTEM.

In recent years, the Hubbard model has been subjected to a renewed attention because of its relevance for High-superconductivity, quantum antiferromagnetism, and ferromagnetism thus playing a central role in theoretical investigations of strongly correlated systems. In this paper, we present a numerical exact diagonalization NED of the Hubbard model and a theoretical exact simulation (TES)with the view to obtaining the groundstate-energy spectrum of two electron interaction on a finite six sites lattice system. The extended Hubbard model with nearest and next-nearest neighbour kinetic hopping terms was first applied on the eigenstates available to the two electrons six sites system. The application of the Hubbard model on the various electron eigenstates generated eigenvalue matrix which was solved by numerical exact diagonalization.  The results of the ground-state energies from the numerical exact diagonalization were compared with the results obtained from the theoretical exact simulation. The comparison of both methods showed that there is a good correlation between the two results. It is established here that there is a strong correlation between the two electrons at very low negative values of the Coulomb interaction strength .Whereas high values of positive Coulomb interaction strength promotes high kinetic energy between two interacting electrons, since the electrons are now free to hop from one atomic site to another.