  Understanding the robustness of topological phases of matter in the presence
of interactions poses a difficult challenge in modern condensed matter, showing
interesting connections to high energy physics. In this work, we leverage these
connections to present a complete analysis of the continuum long-wavelength
description of a generic class of correlated topological insulators:
Wilson-Hubbard topological matter. We show that a Wilsonian renormalization
group (RG) approach, combined with the so-called topological Hamiltonian,
provide a quantitative route to understand interaction-induced topological
phase transitions that occur in Wilson-Hubbard matter. We benchmark two-loop RG
predictions for a quasi-1D Wilson-Hubbard model by means of exhaustive
numerical simulations based on matrix product states (MPS). The agreement of
the RG predictions with MPS simulations motivates the extension of the RG
calculations to higher-dimensional topological insulators.
