Comment on "Exploring chaos in the Dicke model using ground-state fidelity and the Loschmidt echo"

In [PRE $\mathbf{\text{90}}$, 022920 (2014), arXiv:1404.6738] a study of the ground state fidelity of the Dicke model as a function of the coupling parameter is presented. Abrupt jumps of the fidelity in the superradiant phase are observed and are assumed to be related to the transition to chaos. We show that this conclusion results from a misinterpretation of the numerics. In fact, if the parity symmetry is taken into account, the unexpected jumps disappear.