Ultra Cold Fermi Gases In 1D Optical Lattice With Spin-orbit Coupled Based On DMRG

The realization of degenerate Fermi gas, which laid a solid foundation for the realization of the condensation of ultra-cold Fermi gas, made a large number of scholars devote themselves to study ultra-cold Fermi gas. Besides, the realization of spin-orbit coupling provides a new window to study the characteristic of ultra-cold Fermi gas.In this paper, by using the most typical model-Hubbard model in the strong connection system and the density matrix renormalization group(DMRG),which is the most sophisticated calculation method in low dimensional system,we research the effect of the phase transition of ultra-cold Fermi gases loaded on one-dimensional optical lattices when spin-orbit coupling(SOC) and Zeeman field are involved.Firstly, we describe the basics background and progress of the Fermi gas,and introduce degenerate Fermi gas and the basic knowledge of spin-orbit coupling.Then we give a brief introduction of the density matrix renormalization group(DMRG) algorithm and the strong correlation software ALPS(Algorithms and Libraries for Physics Simulations) in the second chapter.secondly, we use the density matrix renormalization group algorithm study the effect of the phase transition of ultra-cold repulsive Fermi gases loaded on one-dimensional optical lattices and superlattices when SOC and Zeeman field are involved. In the one-dimensional optical lattices, It is found that the SOC effects enhance the metal phase and reduce polarization of the system in the presence of both the SOC and a large Zeeman field. And it also suppress the spin density wave state. In addition, when the system keeps a Mott insulation state under the weak spin-orbit coupling, it is figured out that at different SOC strengths, the system appears as different quantum states due to the polarization effect of the Zeeman field. And in the one-dimensional optical superlattices, it is figured out that the SOC effects not only enhance the metal phase and reduce the insulation phase, but it also suppress the bond-charge-density-wave state.Thirdly, we use the density matrix renormalization group algorithm addressthe effect of the phase transition of ultra-cold attract Fermi gases loaded on one-dimensional optical lattices when both SOC and Zeeman field are considered. It turns out that the SOC effects enhance the superfluid phase, and in the non-equilibrium Fermi system, the FFLO phase appears when Zeeman field effect weighs in, while spin-orbit coupling effect not only enforces superfluid phase, also can decrease the FFLO phase.Finally, we summarize the whole paper, and carry on an outlook of the future study in this subject.