  We study the fidelity susceptibility in an antiferromagnetic spin-1 XXZ chain
numerically. By using the density-matrix renormalization group method, the
effects of the alternating single-site anisotropy $D$ on fidelity
susceptibility are investigated. Its relation with the quantum phase transition
is analyzed. It is found that the quantum phase transition from the Haldane
spin liquid to periodic N\'{e}el spin solid can be well characterized by the
fidelity. Finite size scaling of fidelity susceptibility shows a power-law
divergence at criticality, which indicates the quantum phase transition is of
second order. The results are confirmed by the second derivative of the
ground-state energy. We also study the relationship between the entanglement
entropy, the Schmidt gap and quantum phase transitions. Conclusions drawn from
these quantum information observables agree well with each other.
