The Study Of Low-dimensional Ultracold Fermi Gases In Finite-temperature

This thesis focuses on the numerical method for the thermodynamic proper-ties of ultracold Fermi gases in low-dimensional at finite temperature. Based on the thermodynamic Bethe-ansatz equations, we mainly discuss the Fermi Hub-bard model and Fermi Gaudin-Yang model by applying numerical techniques, and we get the corresponding phase diagrams and the physics of thermodynamic quantities.In the first two chapters, we mainly introduce the background of the cold atomic physics and the one-dimensional strongly correlated systems. In the meanwhile, we detail some of the basic cold atomic physics’concepts and some of the important developments in the cold atomic physics research field in recently years. We highlight the importance of the low-dimensional strongly correlated system and it’s research progress, which in turn leads to our research on the study of low-dimensional ultracold Fermi gases in finite-temperature.In the third chapter, we consider the nature of the one-dimensional fermi cold atomic lattice system at finite temperature in the Hubbard model. Based on the thermodynamic Bethe-ansatz equations in the Fermi Hubbard model, we use the numerical method to get the thermodynamic quantities such as the den-sity, energy, entropy, specific heat, compressibility and double occupied and so on. What’s more, we have plot the figures relates to the corresponding thermo-dynamic quantities with the chemical potential gradually changed at different temperatures and interactions. We get the system’s transition figures among the vacuum, fluid phase, Mott insulator phase, fluid phase, and band insulator phase.In the forth chapter, we study the properties of Fermi Gaudin-Yang mod-el in one-dimension by calculating the thermodynamic Bethe-ansatz equations. We get the density, pressure, energy and correlation function with the chemical potential, temperature and interaction. At a given temperature and interaction, we find that there is a quantum critical zone with the thermal fluctuations and quantum fluctuations coexist. We analyze the quantum critical property in this area, which provides the basis for the existence of Luttinger liquid state in a one-dimensional fermi system.Finally, a summary and outlook for our work are given.