  We consider quantum condensed matter systems without particle-number
conservation. Since the particle number is not a good quantum number, states
belonging to different particle-number sectors can hybridize, which causes
topological anticrossings in the spectrum. The resulting spectral gaps support
chiral edge excitations whose wavefunction is a superposition of states in the
two hybridized sectors. This situation is realized in fully saturated
spin-anisotropic quantum magnets without spin conservation, in which single
magnons hybridize with magnon bound pairs, i.e., two-magnon bound states. The
resulting chiral edge excitations are exotic composites that carry mixed
spin-multipolar character, inheriting spin-dipolar and spin-quadrupolar
character from their single-particleness and two-particleness, respectively. In
contrast to established topological magnons, the topological effects discussed
here are of genuine quantum mechanical origin and vanish in the classical
limit. We discuss implications for both intrinsic anomalous Hall-type transport
and beyond-spintronics computation paradigms. We conclude that fully polarized
quantum magnets are a promising platform for topology caused by hybridizations
between particle-number sectors, complementing the field of ultracold atoms
working with a conserved number of particles.
