  The conserved Swift-Hohenberg equation (or Phase-Field-Crystal [PFC] model)
provides a simple microscopic description of the thermodynamic transition
between fluid and crystalline states. Combining it with elements of the
Toner-Tu theory for self-propelled particles Menzel and L\"owen [Phys. Rev.
Lett. 110, 055702 (2013)] obtained a model for crystallization (swarm
formation) in active systems. Here, we study the occurrence of resting and
traveling localized states, i.e., crystalline clusters, within the resulting
active PFC model. Based on linear stability analyses and numerical continuation
of the fully nonlinear states, we present a detailed analysis of the
bifurcation structure of periodic and localized, resting and traveling states
in a one-dimensional active PFC model. This allows us, for instance, to explore
how the slanted homoclinic snaking of steady localized states found for the
passive PFC model is amended by activity. A particular focus lies on the onset
of motion, where we show that it occurs either through a drift-pitchfork or a
drift-transcritical bifurcation. A corresponding general analytical criterion
is derived.
