| Since Bose-Einstein condensation was realized experimentally in 1995,the properties of this matter have been widely studied.With the development of research,more and more physical factors was considered,from the ideal gas model at the beginning to the atomic condensation model under the harmonic trap potential,from the weak interaction model to the strong interaction model,and so on.The rich physical results are obtained.At present,the spin-orbit coupling of atoms has become a hot research topic,which leads to different matter phases in atomic condensates.In this paper,based on the one-dimensional Hubbard model,the harmonic trap potential and spin-orbit coupling are considered to investigate the ground state characteristics of the repulsive Fermi gas in the optical lattice.This paper firstly introduces some basis concepts about Bose-Einstenin condensation and degenerate Fermi gases.The brief introductions of the ALPS(Algorithms and Libraries for Physics),a strong correlation simulation algorithm and DMRG(Density Matrix Renormalization Group)of ALPS are given.The ground-state properties of polarized Fermi gas in a one-dimensional optical lattice are calculated by using the DMRG method to prove the method being precision and practicability.Secondly,DMRG algorithm in ALPS software is used to study the pairing correlation and superfluidity of one-dimensional Hubbard model.The mains are as follows:(1)In the one-dimensional Hubbard model with harmonic trap potential,we explore the effect of the harmonic trap potential and repulsive interaction on the pairing correlation and superfluidity.The harmonic trap potential and repulsive interaction have the opposite effects on the particle distribution.On the one hand,the harmonic trap potential causes the particles to gather near the center of the potential well,on the other hand,the coulomb repulsive interaction causes the particles to repel and disperse each other.When V is large enough,the system is in double occupied state.In contrast,when the repulsive interaction is stronger,the repulsive interaction excludes the possibility of the double occupied state,and the density distribution of particles appears a flat region occupying a particle at a lattice point,which is called Mott insulate state.It is found that when the occupied number of particles is less than half filled and U is greater than a critical value,the system is in Mott insulate state at the center of potential well,while cooper pairs appear at the edge,showing the existence of the superfluidity.However,as the total number of lattice points increases and the repulsive interaction increases,the binding energy between two Fermi atoms with opposite spins becomes negative,and the system is in a superfluidity,but no Mott insulate state appears in the center of potential well.As the repulsive interaction continues to grow,whether there is a Mott insulate state,the system can have superfluidity.(2)In the one-dimensional Hubbard model with harmonic trap potential and spin-orbit coupling,we explore the effect of the harmonic trap potential,repulsive interaction and spin-orbit coupling on the pairing correlation and the superfluidity.It is found that when the occupied number of particles is less than half,the spin-orbit coupling enhances the metallic property when the system is the metallic state.When the system is in Mott insulate state,the spin-orbit coupling weakens the insulation and has superfluidity.When the occupied number of particles is equal to half,the region of Fermi superfluidity decreases.When the occupied number of particles is greater than half,neither Fermi superfluidity nor pairing exists.At the same time,we find that the change of spin-orbit coupling has little influence on the above conclusion.Finally,we summarize the whole paper and envision the next work. |
