  We present a theory for the two kinds of dynamical quantum phase transitions,
termed DPT-I and DPT-II, based on a minimal set of symmetry assumptions. In the
special case of collective systems with infinite-range interactions, both are
triggered by excited-state quantum phase transitions. For quenches below the
critical energy, the existence of an additional conserved charge, identifying
the corresponding phase, allows for a nonzero value of the dynamical order
parameter characterizing DPTs-I, and precludes the main mechanism giving rise
to nonanalyticities in the return probability, trademark of DPTs-II. We propose
a statistical ensemble describing the long-time averages of order parameters in
DPTs-I, and provide a theoretical proof for the incompatibility of the main
mechanism for DPTs-II with the presence of this additional conserved charge.
Our results are numerically illustrated in the fully-connected transverse-field
Ising model, which exhibits both kinds of dynamical phase transitions. Finally,
we discuss the applicability of our theory to systems with finite-range
interactions, where the phenomenology of excited-state quantum phase
transitions is absent. We illustrate our findings by means of numerical
calculations with experimentally relevant initial states.
