Fidelity approach to Gaussian transitions

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