  Here we analyze the divergences of the irreducible vertex function in
dynamical mean field theory, which may indicate either a non-physical breakdown
of the perturbation theory or a response to some physical phenomenon. To
investigate this question, we construct a quasiparticle vertex from the
diverging irreducible vertex functions. This vertex describes the scattering
between quasiparticles and quasiholes in a Fermi liquid. We show that the
quasparticle vertex \textit{does not} diverge in the charge channel, wherein
the irreducible vertex \textit{does} diverge; and we show that the
quasiparticle vertex does diverge in the spin channel, wherein the irreducible
vertex does not diverge. This divergence occurs at the Mott transition wherein
the Fermi liquid theory breaks down. Both Hubbard and Anderson lattices are
investigated. In general, our results support that the divergences of the
irreducible vertex function do not indicate a non-physical failure of the
perturbation theory. Instead, the divergences are the mathematical consequence
of inverting a matrix (the local charge susceptibility) which accumulates
increasingly negative diagonal elements as the Hubbard interaction suppresses
charge fluctuations. Indeed, we find that the first symmetric divergences of
the irreducible vertex in both Hubbard and Anderson lattices occurs near the
maximum magnitude of the (negative) vertex-connected part of the charge
susceptibility, which suppresses charge fluctuations.
