Phase Separations in the Narrow-Bandwidth Limit of the Penson-Kolb-Hubbard Model at Zero Temperature

In this work we study the ground state of the Penson-Kolb-Hubard model in the limit of narrow-bandwidth. We present phase diagrams of the model for fixed chemical potential and concentration (involving various phase separations). The results are derived within the Hartree-Fock approximation (HFA) in the narrow-bandwidth regime and compared with the exact ones in the atomic limit and the high-dimension regime. Our investigation reveals that the HFA can reconstruct the exact diagram at the ground state when the bandwidth approaches to zero.