  Two-dimensional topological insulators possess conducting edge states at
their boundary while being insulating in the bulk. The detection of edge states
remains an open question in ultracold atom setups. We propose a configuration
to implement a topological interface within the experimentally realizable
time-reversal invariant Hofstadter model which gives rise to a topological
phase boundary at the center of the system, and investigate the influence of
two-body interactions on the interface in a fermionic system. The interface can
in principle be probed via the spatially resolved compressibility of the system
by using a quantum gas microscope. Furthermore, we distinguish the phases
through their Hall response and compute a local spin Chern marker which proves
the phase separation of two distinct topological many-body phases. The
bulk-boundary correspondence for the interacting system is confirmed by
computing the edge state spectra at the interface.
