  We show that for quantum phase transitions with a single bosonic zero mode at
the critical point, like the Dicke model and the Lipkin-Meshkov-Glick model,
metric quantities such as fidelity, that is, the overlap between two ground
states corresponding to two values $\lambda_1$ and $\lambda_2$ of the
controlling parameter $\lambda$, only depend on the ratio
$\eta=(\lambda_1-\lambda_c)/(\lambda_2-\lambda_c)$, where $\lambda=\lambda_c$
at the critical point. Such scaling property is valid also for time-dependent
quantities such as the Loschmidt echo, provided time is measured in units of
the inverse frequency of the critical mode.
