  We investigate the effects of electronic correlations on the
Bernevig-Hughes-Zhang model using the real-space density matrix renormalization
group (DMRG) algorithm. We introduce a method to probe topological phase
transitions in systems with strong correlations using DMRG, substantiated by an
unsupervised machine learning methodology that analyzes the orbital structure
of the real-space edges. Including the full multi-orbital Hubbard interaction
term, we construct a phase diagram as a function of a gap parameter ($m$) and
the Hubbard interaction strength ($U$) via exact DMRG simulations on $N\times
4$ cylinders. Our analysis confirms that the topological phase persists in the
presence of interactions, consistent with previous studies, but it also reveals
an intriguing phase transition from a paramagnetic to an antiferromagnetic
topological insulator. The combination of the magnetic structure factor,
strength of magnetic moments, and the orbitally resolved density, provides
real-space information on both topology and magnetism in a strongly correlated
system.
