  Using molecular dynamics simulation, we investigate the slow dynamics of a
supercooled binary mixture of soft particles interacting with a generalized
Hertzian potential. At low density, it displays typical slow dynamics near its
glass transition temperature. At higher densities, particles bond together,
forming clusters, and the clusters undergo the glass transition. The number of
particles in a cluster increases one by one as the density increases. We
demonstrate that there exist the multiple cluster-glass phases characterized by
a different number of particles per cluster, each of which is separated by
distinct minima. Surprisingly, a so-called higher order singularity of the
mode-coupling theory signaled by a logarithmic relaxation is observed in the
vicinity of the boundaries between monomer and cluster glass phases. The system
also exhibits rich and anomalous dynamics in the cluster glass phases, such as
the decoupling of the self- and collective dynamics.
