  We investigate the interacting, one-dimensional Rice-Mele model, a
prototypical fermionic model of topological properties. To set the stage, we
firstly compute the single-particle spectral function, the local density, and
the boundary charge in the absence of interactions. The boundary charge is
fully determined by bulk properties indicating a bulk-boundary correspondence.
In a large parameter regime it agrees with the one obtained from an effective
low-energy theory (arXiv:2004.00463). Secondly, we investigate the robustness
of our results towards two-particle interactions. To resum the series of
leading logarithms for small gaps, which dismantle plain perturbation theory in
the interaction, we use an essentially analytical renormalization group
approach. It is controlled for small interactions and can directly be applied
to the microscopic lattice model. We benchmark the results against numerical
density matrix renormalization group data. The main interaction effect in the
bulk is a power-law renormalization of the gap with an interaction dependent
exponent. The important characteristics of the boundary charge are unaltered
and can be understood from the renormalized bulk properties, elevating the
bulk-boundary correspondence to the interacting regime. This requires a
consistent treatment not only of the low-energy gap renormalization but also of
the high-energy band width one. In contrast to low-energy field theories our
renormalization group approach also provides the latter. We show that the
interaction spoils the relation between the bulk properties and the number of
edge states, consistent with the observation that the Rice-Mele model with
finite potential modulation does not reveal any zero-energy edge states.
