A VARIATIONAL THEORY OF QUASI-PARTICLES IN A 3D N x N x N CUBIC LATTICE

The single-band Hubbard Hamiltonian study faces a serious limitation and difficulty as we move away from finite - size lattices to larger N - dimensional lattices. Thus there is the need to develop the means of overcoming the finite - size lattice defects as we pass on to a higher dimension. In this work, a quantitative approximation to the one-band Hubbard model is presented using a variational analytic approach. The goal of this work, therefore, is to explore quantitatively the lowest ground-state energy and the pairing correlations in 3D N x N x N lattices of the Hubbard model. We developed the unit step model as an approximate solution to the single-band Hubbard Hamiltonian to solve variationally the correlation of two interacting elections on a three-dimensional cubic lattice. We also showed primarily how to derive possible electronic states available for several even and odd3D lattices, although, this work places more emphasis on a 3D 5 x 5 x 5 lattice. The results emerging from our present study compared favourably with the results of Gutzwiller variational approach (GVA) and correlated variational approach (CVA), at the large limit of the Coulomb interaction strength (U/4t). It is revealed in this study, that the repulsive Coulomb interaction which in part leads to the strong electronic correlations, would indicate that the two electron system prefer not to condense into s-wave superconducting singlet state (s = 0), at high positive values of the interaction strength.