Hubbard model In Square Lattices: A Mean-field Hartree-fock Approach

Abstract

This thesis is mainly an effort to reproduce the well-known results that HartreeFock approximation gives for the Hubbard Model in two dimensions. As the area of application magnetic phases in the finite-size square lattices was chosen. The reason of choosing this particular area is that in the sources we went through mean-field theory was used only for examining the magnetic phases for rectangular density of state not for the actual density of states of a square lattice. We used the mean-field Hartree-Fock approximation and obtained the phase diagrams for the paramagnetic, ferromagnetic, charge density wave (CDW) and spin density wave (SDW) phases. The antiferromagnetic phase was found to be a special kind of the SDW phase. The hamiltonians used for the ferromagnetic and paramagnetic cases were identical. However because of the non-diagonal correlations present in the system the CDW and SDW hamiltonian was different.