  Spin lattice models play central role in the studies of quantum magnetism and
non-equilibrium dynamics of spin excitations -- magnons. We show that a spin
lattice with strong nearest-neighbor interactions and tunable long-range
hopping of excitations can be realized by a regular array of laser driven
atoms, with an excited Rydberg state representing the spin-up state and a
Rydberg-dressed ground state corresponding to the spin-down state. We find
exotic interaction-bound states of magnons that propagate in the lattice via
the combination of resonant two-site hopping and non-resonant second-order
hopping processes. Arrays of trapped Rydberg-dressed atoms can thus serve as a
flexible platform to simulate and study fundamental few-body dynamics in spin
lattices.
