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We thoroughly analyze the divergences of the irreducible vertex functionsoccurring in the charge channel of the half-filled Hubbard model in closeproximity to the Mott metal-insulator transition (MIT). In particular, bysystematically performing dynamical mean-field theory (DMFT) calculations onthe two-particle level, we determine the location and the number of the vertexdivergences across the whole coexistence region adjacent to the first-ordermetal-to-insulator transition. We find that the lines in the parameter space,along which the vertex divergences occur, display a qualitatively differentshape in the coexisting metallic and insulating phase, which is also associatedto an abrupt jump of the number of divergences across the MIT. Physically, thesystematically larger number of divergences on the insulating side of thetransition reflects the sudden suppression of local charge fluctuation at theMIT. Further, a systematic analysis of the results demonstrates that the numberof divergence lines increases as a function of the inverse temperature${\beta\!=\!(k_\mathrm{B} T)^{-1}}$ by approaching the Mott transition in thezero temperature limit. This makes it possible to identify the zero-temperatureMIT as an accumulation point of an infinite number of vertex divergence lines,unveiling the highly nonperturbative nature of the underlying transition.

Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region