  Traditionally, skyrmions are treated as continuum magnetic textures of
classical spins with a well-defined topological skyrmion number. Owing to their
topological protection, skyrmions have attracted great interest as building
blocks in future memory technology. Smaller skyrmions offer greater memory
density, however, quantum effects are not negligible for skyrmions with sizes
of just a few lattice constants. In this paper we study quantum fluctuations
around dense skyrmion crystal ground states, and focus on the utility of a
discretized order parameter for quantum skyrmions. The order parameter is found
to be a useful indicator of the existence of quantum skyrmions, and captures
the quantum phase transition between two distinct skyrmion phases.
