THE TWO-ELECTRON INTERACTION IN THE GROUND STATE OF THE t-U-V-J MODEL

ABSTRACT
A detailed and quantitative study is presented of the behaviour of two interacting electrons on a lattice using a single band tight binding model with a kinetic term t, on-site Coulomb term U,
nearest neighbour (NN) Coulombic term V, and NN exchange interaction term J (the so called t-U-V-J Hamiltonian).
The dynamics of the interacting electronic pair is described in this work by the single band t-U-V-J model which is hoped to provide insight into the interaction mechanism of strongly correlated electron systems (Amadon and Hirsch, 1996; Vollhardt et al., 2000). Although the Hubbard model (which is the t-U Hamiltonian) was originally proposed as a simple model to describe the physics of ferromagnetism in metals, the various studies in the literature show that the Hamiltonian model with only NN hopping and on-site Coulomb interaction usually favours antiferromagnetism (Hirsch, 1989; Petukhov et al.1992; Amadon and Hirsch, 1996; Ulmke, 2000). Three natural ways to go beyond the original Hubbard model are to include other interaction matrix elements within the single band model, or enhance the kinetic part or include band degeneracy that allows intra-atomic exchange. The first situation is investigated in this present work by developing and using a highly simplified formulation of the correlated
variational approach (CVA). This approach, which is an approximation technique, is applied to study the dynamics of two interacting electrons on one dimensional (1D), two dimensional (2D) and three dimensional (3D) finite sized lattices with periodic boundary conditions.
The results obtained show that the J term plays the domineering role in the dynamics leading to the transition from  antiferromagnetism to ferromagnetism, the U term enhances the
tendency to this transition but cannot on its own induce it, and the V term suppresses the tendency to this transition. This was the same observation made from the numerical exact diagonalization
study of 1D lattices by Amadon and Hirsch (1996). In this thesis, the effects of band filling, and higher dimensionality, and the role of even or odd number of lattice sites on the various
parameters at the transition point are analyzed. Thus this study is able to develop and utilize a highly simplified correlated variational approach (HSCVA) to provide detailed insight into the
behaviour of highly correlated electron systems by clearly delineating the parameter space for the different physics accessible to the t-U-V-J potential. In particular, detailed conditions for the occurrence of a transition from an antiferromagnetic phase to a ferromagnetic phase are discussed.