  We study dynamical phase transitions (DPTs) in quantum many-body systems with
infinite-range interaction, and present a theory connecting the two kinds of
known DPTs (sometimes referred to as DPTs-I and DPTs-II) with the concept of
excited-state quantum phase transition (ESQPT), traditionally found in
collective models. We show that DPTs-I appear as a manifestation of symmetry
restoration after a quench from the broken-symmetry phase, the limits between
these two phases being demarcated precisely by an ESQPT. We describe the order
parameters of DPTs-I with a generalization of the standard microcanonical
ensemble incorporating the information of an additional conserved charge
identifying the corresponding phase. We also show that DPTs-I are linked to a
mechanism of information erasure brought about by the ESQPT, and quantify this
information loss with the statistical ensemble that we propose. Finally, we
show analytically that DPTs-II are forbidden in these systems for quenches
leading a broken-symmetry initial state to the same broken-symmetry phase, on
one side of the ESQPT, and we provide a formulation of DPTs-II depending on the
side of the ESQPT where the quench ends. We analyze the connections between
various indicators of DPTs-II. Our results are numerically illustrated in the
infinite-range transverse-field Ising model and are applicable to a large class
of collective quantum systems satisfying a set of conditions.
