Hartree-Fock mean field theory analysis of the two-species Kagome lattice Hubbard model

Mean field theory techniques have been and continue to be widely applied in the study of strongly correlated many-body systems. The advantage of mean field theory stems from its ability to provide qualitative, and sometimes quantitative, information on the tendency of the many-body system to develop ordered phases when other theoretical methods might be challenging to apply. We apply an unrestricted Hartree-Fock mean field theory analysis to investigate the quantum phases and phase transitions of a Kagome lattice Hubbard model with a heterogeneous basis. By a heterogeneous basis we mean the presence of two species of atoms on each triangular plaquette of the Kagome lattice. We consider a set of anisotropic couplings (first and second neighbor hopping) and the Hubbard interaction. We focus on both the charge and magnetic degrees of freedom of fermions to compute the charge density, structure factor, and magnetization as the couplings are varied. The ordered magnetic phases that we find are compared to the strong-coupling results of the model. We also discuss possible extensions to the bilayer Kagome case of the two-species model.