  Topological insulating phases are primarily associated with condensed-matter
systems, which typically feature short-range interactions. Nevertheless, many
realizations of quantum matter can exhibit long-range interactions, and it is
still largely unknown the effect that these latter may exert upon the
topological phases. In this Letter, we investigate the Su-Schrieffer-Heeger
topological insulator in the presence of long-range interactions. We show that
this model can be readily realized in quantum simulators with trapped ions by
means of a periodic driving. Our results indicate that the localization of the
associated edge states is enhanced by the long-range interactions, and that the
localized components survive within the ground state of the model. These
effects could be easily confirmed in current state-of-the-art experimental
implementations.
