According to the exact analytical Bethe-ansatz solution of the one-dimensional spin-l/2 XXZ model, we perform a numerical study of one-dimensional spinless fermions in an optical lattice in the presence of harmonic potential by using a local density approximation. We study the density profile, and obtain the p-u phase diagram （here p = N√v2/t is the characteristic dimensionless density and u = V/t is the interaction strength scaled in units of the hopping parameter t）. With the increases of particle density and nearest-neighbour interaction, the system undergoes five different quantum phases. Through calculating the thermodynamic stiffness Sp, we find that it can be used as an order parameter. Its singular points can measure the quantum phase transitions in such a confined system.%本文借助于一维自旋1／2-XXZ模型的Bethe—ansatz精确解，利用局域密度近似（LDA），讨论了谐振势中一维无自旋费米子的密度分布，得出了芦“相图（这里的芦为无量纲的粒子数密度变量，u为相互作用强度）．对相图的分析表明，随着原子密度和近邻相互作用的变化，系统出现五个不同的混合量子相．通过对热力学硬度Sp的计算，发现其可作为体系的序参量，其奇异点可用以度量受限体系中量子相变的发生．
展开▼
