  The existence or absence of non-analytic cusps in the Loschmidt-echo return
rate is traditionally employed to distinguish between a regular dynamical phase
(regular cusps) and a trivial phase (no cusps) in quantum spin chains after a
global quench. However, numerical evidence in a recent study [J. C. Halimeh and
V. Zauner-Stauber, arXiv:1610.02019] suggests that instead of the trivial phase
a distinct anomalous dynamical phase characterized by a novel type of
non-analytic cusps occurs in the one-dimensional transverse-field Ising model
when interactions are sufficiently long-range. Using an analytic semiclassical
approach and exact diagonalization, we show that this anomalous phase also
arises in the fully-connected case of infinite-range interactions, and we
discuss its defining signature. Our results show that the transition from the
regular to the anomalous dynamical phase coincides with Z2-symmetry breaking in
the infinite-time limit, thereby showing a connection between two different
concepts of dynamical criticality. Our work further expands the dynamical phase
diagram of long-range interacting quantum spin chains, and can be tested
experimentally in ion-trap setups and ultracold atoms in optical cavities,
where interactions are inherently long-range.
