Average modulus fidelity versus average level spacing (energy density) for 1D hard-core boson system with (a) t′ = V′ = 0.0 and (b) t′ = V′ = 1.0. Average level spacings are obtained by where and are the two ends of energy spectrum. The size of the subspace N is taken to be 506, 1463, 1771, 4389, and 7084.