  We address the effect of nearest-neighbor (NN) interactions on the
topological properties of the Su-Schrieffer-Heeger (SSH) chain, with
alternating hopping amplitudes t1 and t2. Both numerically and analytically, we
show that the presence of interactions induces phase transitions between
topologically different regimes. In the particular case of one-hole excitations
in a half-filled SSH chain, the V=t2 vs. t1=t2 phase diagram has topological
phases at diagonal regions of the phase plane. The interaction acts in this
case as a passivation potential. For general filling of the SSH chain,
different eigensubspaces of the SSH Hamiltonian may be classified as
topologically trivial and non-trivial. The two-hole case is studied in detail
in the large interaction limit, and we show that a mapping can be constructed
of the two-hole SSH eigensubspaces into one-particle states of a
non-interacting one-dimensional (1D) tight-binding model, with interfaces
between regions with different hopping constants and local potentials. The
presence of topological edge states in the equivalent chain can be readily
identifed, as well as their correspondence to the original two-hole states.
Furthermore, we found that the presence of the NN interaction generates a state
where two holes occupy two consecutive edge states. Such many-body states
should also occur for arbitrary filling leading to the possibility of a
macroscopic hole gathering at the surface (at consecutive edge states).
