Magnetic Phase Diagram in the Periodic Anderson Model (PAM): An Exact Diagonalization Approach (Published)
A detailed and qualitative matrix representation of the one-dimensional periodic Anderson model (PAM) is presented giving the ground state as a function of band filling using the exact diagonalization technique.The simplest lattice system of two electrons on two sites is consider, in the study the results of the matrix element were compared and it was found that for the symmetric case where the energy of the f electrons Ef =-U/2 and the hybridization matrix element V switched off, the results are consistent with the Kondo model Hamiltonian matrix in the J =0 region.The results obtained in the study are also in agreement with the famous Hubbard (t –u) model if the Hybridization term V of the PAM and the energy of the localized f orbital Ef are switched off. The results of the ground state energies were used to determine the transition from antiferromagnetic (AFM) phase to a ferromagnetic (FM) phase and vice versa.
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. The Hubbard model used in this research describes interacting electrons in narrow energy bands, with application to problems as diverse as high – Tc superconductivity, band magnetism and the metal-insulator transition. This research seeks to solve one of the most challenging problems in Theoretical physics which is to describe electronic correlations. In this research the t – U Hubbard model is used to solve analytically and numerically using the exact diagonalization techniquesThis research work focused on the spin interaction and magnetic behavior of some systems and it is therefore an investigation into the various phenomena seen in the phase diagram of ferromagnetic systems. We studied the 2 electrons on 2 sites, 2 electrons on 3 sites and 2 electrons on 4 sites all in One-Dimension (1-D), where the onsite coulomb repulsion, U, and the hopping matrix element, t, were varies to determine their magnetic phase diagram.This results obtained shows that, as the values of the onsite coulomb repulsion, U, increases in all the lattice systems studied, the electronic correlation that favours ferromagnetism gets stronger, but there were no clear transition, and at some point the lattices loss its antiferromagnetic properties, hence the instability of ferromagnetism were established. It was also observed that as the hopping matrix element, t, increases the electronic correlation that favours ferromagnetism get stronger and the lattice begins to loss antiferromagnetic properties but beyond the transition point the lattice began to gain a much stronger antiferromagnetism, hence the ferromagnetism is unstable.