One-dimensional spinless fermions in a confined system
受限一维无自旋费米子系统的性质研究

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= Nf（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 Sρ,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.