THEORETICAL EXACT CALCULATION OF THE GROUNDSTATE ENERGIES OF TWO ELECTRON INTERACTION IN 1D FOUR SITES SYSTEM
Keywords:
total energies, ground-state energies, density-density interaction, Coulomb interaction strength, Hubbard model, Electron correlationAbstract
There has been dramatic progress in the development of electron correlation techniques for the accurate treatment of atomic structures and energies of molecules. In this study, we consider a theoretical exact method for obtaining the ground-state energies of two interacting electrons on a one-dimensional four sites lattice system. We first applied the extended Hubbard model with nearest and next-nearest neighbour to act on the various electron sites available to the two electrons four sites lattice. The application of the Hubbard model on the electron states produced an 16x16 eigen value matrix which was solved by analytical exact diagonalization. The
results of the ground-state energies from the theoretical exact method are compared with the ones obtained from the analytical exact diagonalization. The results compared favourably with one another. It is established here that there is a strong correlation between the two electrons at high negative values of the Coulomb interaction strength ????/????????. It is also shown in this study that the −???? + ???? + ????extended Hubbard model is a better model to study correlation process and the ground-state energies it produced is minimum compared to the other forms of the Hubbard model.
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