The Study Of Density Function Theory On One-dimensional Lattice Systems

In this paper, the ground-state properties of one-dimensional strongly correlated systems are studied, for example the spin-1/2 XXZ model and the one-dimensional attractive Hubbard model. Firstly, we explain the definition, and the significance of 1D strongly correlated systems then we show some integrable models and the common numerical methods:The main purpose of this paper is to study the ground-state properties of 1D spin-1/2 XXZ model and the attractive Hubbard model. We obtained the ground state energy, chemical potential and the exchange-correlation (xc) potential of the 1D spin-1/2 XXZ model. The density distribution and the Phase diagram of the 1D spin-1/2 XXZ model with confinement are discussed, after that we study the phase transition of the confined system.We also calculate the xc potential of the 1D attractive Hubbard model by spin-density-functional theory. The influences of the external potential, system size, and the interaction on the ground-state properties are discussed. Comparing the numerical results of the spin-density-functional theory with those of density-matrix renormalization group, we conclude that, when the interaction is not very strong, we can get the satisfactory results easily by the spin-density-functional theory. In addition, we define the characteristic particle density where Nf is the particle number V2 is the external potential t describe the hopping between lattices), and obtain theρ-u phase diagram. (u-U/t). At the same time the phase transition can be exactly reflected by the double occupancy, its derivative and the compressibility, stiffness, and fidelity. From the results we confirmed that comparing with other numerical results, for example the density-matrix renormalization group, the ground-state properties of the 1D strongly correlated system under confinement can be captured by the density-functional theory.