  We study the Loschmidt echo and the dynamical free energy of the Anderson
model after a quench of the disorder strength. If the initial state is extended
and the eigenstates of the post-quench Hamiltonian are strongly localized, we
argue that the Loschmidt echo exhibits zeros periodically with the period $2\pi
/D$ where $D$ is the width of spectra. At these zeros, the dynamical free
energy diverges in a logarithmic way. We present numerical evidence of our
argument in one- and three-dimensional Anderson models. Our findings connect
the dynamical quantum phase transitions to the localization-delocalization
phase transitions.
