The Research Of Phase Transition In Spin Orbit Coupling Based On DMRG Algorithm To Ultracold Fermi Gas

In this paper, we using the density-matrix renormalization group (DMRG) to study the phase transition of Fermi gas under the influence of the spin orbit coupling and the Zeeman field in optical lattice and superlattice.First of all, we study the one-dimensional reject Fermi gas in the optical lattice and superlattice, as the spin orbit coupling in the Mott insulation state, Band insulation state, charge density wave (BCDW) state, and Mptt insulation system, found that all of the state transition into metal phase. We used phase diagram clearly reflects the whole phase change process of system.Then we went on to study the phase transition of one-dimensional attract Fermi gas under the spin orbit coupling and Zeeman field in the optical lattice,When the spin orbit coupling on the Band insulation alone, the system have taken place phase transition between the Band insulation state and the BCS superfluid state; When the Zeeman field effect on the Band insulation state alone, system has no obvious place phase; The Zeeman field and spin orbit coupling on the Band insulation insulation, found that the particle number density distribution appear obvious oscillation, and there is polarization, the system have taken place phase transition between the Band insulation state and BCS superfluid state.Finally, the spin orbit coupling on the BCS superfluid state alone, system has no obvious place phase; The Zeeman effect on the BCS superfluid insulation alone, found that the correlation function appear periodic oscillation, the system have taken place phase transition between the BCS superfluid insulation and FFLO insulation; The Zeeman and spin orbit coupling on the BCS superfluid insulation, we found that the polarization decreases, the system have taken place phase transition between the FFLO state and the BCS superfluid state. From the above content,it show that the spin orbit coupling can compresse FFLO state and suppress phase separation. Finally, we clearly reflects the all phase transformation through the h-n phase diagram.