Fidelity approach to Gaussian transitions

Abstract

The fidelity approach to the Gaussian transitions in spin-one $\mathit{XXZ}$ spin chains with three different values of Ising-type anisotropy $\ensuremath{\lambda}$ 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 $\ensuremath{\lambda}=2.59$ and 1, the fidelity susceptibility fails to detect the Gaussian transition for $\ensuremath{\lambda}=0.5$. Thus our results demonstrate the limitation of the fidelity susceptibility in characterizing quantum phase transitions, which was proposed recently in general frameworks.