  The fidelity approach to the Gaussian transitions in spin-one XXZ spin chains
with three different values of Ising-like anisotropy lambda is analyzed by
means of the density matrix renormalization group (DMRG) technique for systems
of large sizes. We find that, despite the success in the cases of lambda=2.59
and 1, the fidelity susceptibility fails to detect the Gaussian transition for
lambda=0.5. Thus our results demonstrate the limitation of the fidelity
susceptibility in characterizing quantum phase transitions, which was proposed
recently in general frameworks.
