  Strong mutual interactions correlate elementary excitations of quantum matter
and plays a key role in a range of emergent phenomena, from binding and
condensation to quantum thermalization and many-body localization. Here, we
employ a Rydberg quantum simulator to experimentally demonstrate strongly
correlated spin transport in anisotropic Heisenberg magnets, where the
magnon-magnon interaction can be tuned two orders of magnitude larger than the
magnon hopping strength. In our approach, the motion of magnons is controlled
by an induced spin-exchange interaction through Rydberg dressing, which enables
coherent transport of a single Rydberg excitation across a chain of
ground-state atoms. As the most prominent signature of a giant anisotropy, we
show that nearby Rydberg excitations form distinct types of magnon bound
states, where a tightly bound pair exhibits frozen dynamics in a fragmented
Hilbert space, while a loosely bound pair propagates and establishes
correlations beyond a single lattice site. Our scheme complements studies using
resonant dipole-dipole interactions between Rydberg states, and opens the door
to exploring quantum thermodynamics with ultrastrong interactions and kinetic
constraints.
