  We present a quantitative analysis of two-particle interaction effects in
generalized, one-dimensional Aubry-Andr\'e-Harper models with the Fermi energy
placed in one of the band gaps. We investigate systems with periodic as well as
open boundary conditions; for the latter focusing on the number of edge states
and the boundary charge. Both these observables are important for the
classification of noninteracting topological systems. In our first class of
models the unit cell structure stems from periodically modulated
single-particle parameters. In the second it results from the spatial
modulation of the two-particle interaction. For both types of models, we find
that the single-particle band gaps are renormalized by the interaction in
accordance with expectations employing general field theoretical arguments.
While interaction induced effective edge states can be found in the local
single-particle spectral function close to a boundary, the characteristics of
the boundary charge are not modified by the interaction. This indicates that
our results for the Rice-Mele and Su-Schriefer-Heeger model [Phys. Rev. B 102,
085122 (2020)] are generic and can be found in lattice models with more complex
unit cells as well.
