The demixing of the two-component fermions in optical lattices under a spin-dependent external potential

The demixing of two-component fermions in optical lattices under a spin-dependent external potential is investigated using the density-matrix renormalization group method. The influence of on-site interactions (u) and the ratio of the spin-dependent external potentials ($\gamma$) on the demixing is discussed. The $\gamma-u$ state diagram is numerically mapped out, from which we distinguish the phase-mixed region from the phase-separated one. A minimum point appears in the phase boundary. On the right part of the point an insulating core is formed in the spin-up densities during the demixing, while on the left one only metallic phase exists.