  We study two-particle states in a Su-Shrieffer-Heeger (SSH) chain with
periodic boundary conditions and nearest-neighbor (NN) interactions. The system
is mapped into a problem of a single particle in a two-dimensional (2D) SSH
lattice with potential walls along specific edges. The 2D SSH model has a
trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D)
topological invariant, along specific directions of the lattice, which allow
for the presence of topological edge states. Using center-of-mass and relative
coordinates, we calculate the energy spectrum of these two-body states for
strong interactions and find that, aside from the expected appearance of
doublon bands, two extra in-gap bands are present. These are identified as
bands of topological states localized at the edges of the internal coordinate,
the relative distance between the two particles. As such, the topological
states reported here are intrinsically many-body in what concerns their real
space manifestation, having no counterpart in single-particle states derived
from effective models. Finally, we compare the effect of Hubbard interactions
with that of NN interactions to show how the presence of the topological bound
states is specific to the latter case.
