(a) Typical localized wave function when the harmonic trap presents. (b) Local average density as a function of δ without disorders (V_r = 0). Fermion number N = 600. Other parameters are the same as that in Fig. 2. (c) Corresponding energy spectrum as a function of δ with periodic boundary condition. (d) Relationships between the sizes of energy gaps and the widths of the density plateaus with different strengths of disorders. Here, δ = π and V_r = 0, 0.25, 0.5, 0.75, 1, and 2. The V_r increases along the directions of the arrows.