受限一维无自旋费米子系统的性质研究

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ρ-u相图(这里的ρ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S_ρ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

One-dimensional spinless fermions in a confined system

According to the exact analytical Bethe-ansatz solution of the one-dimensional spin-1/2 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 theρ-u phase diagram(hereρ= N_f（V₂/t）^1/2 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 S_ρ,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.