  Over the recent years coherent, time-periodic modulation has been established
as a versatile tool for realizing novel Hamiltonians. Using this approach,
known as Floquet engineering, we experimentally realize a long-ranged,
anisotropic Heisenberg model with tunable interactions in a trapped ion quantum
simulator. We demonstrate that the spectrum of the model contains not only
single magnon excitations but also composite magnon bound states. For the
long-range interactions with the experimentally realized power-law exponent,
the group velocity of magnons is unbounded. Nonetheless, for sufficiently
strong interactions we observe bound states of these unconventional magnons
which possess a non-diverging group velocity. By measuring the configurational
mutual information between two disjoint intervals, we demonstrate the
implications of the bound state formation on the entanglement dynamics of the
system. Our observations provide key insights into the peculiar role of
composite excitations in the non-equilibrium dynamics of quantum many-body
systems.
