Scaling properties of fidelity in the spin-1 anisotropic model

By means of the density matrix renormalization group technique, the scaling relation of the fidelity susceptibility proposed recently is verified for the spin-one $XXZ$ spin chain with an on-site anisotropic term. Moreover, from the results of both the fidelity susceptibility and the entanglement entropy, the critical points and some of the corresponding critical exponents are determined through a proper finite-size scaling analysis, and these values agree with the findings in the literature. Thus our work provides a numerical support of the use of the fidelity in detecting quantum phase transitions.