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Here we analyze the divergences of the irreducible vertex function indynamical mean field theory, which may indicate either a non-physical breakdownof the perturbation theory or a response to some physical phenomenon. Toinvestigate this question, we construct a quasiparticle vertex from thediverging irreducible vertex functions. This vertex describes the scatteringbetween quasiparticles and quasiholes in a Fermi liquid. We show that thequasparticle vertex \textit{does not} diverge in the charge channel, whereinthe irreducible vertex \textit{does} diverge; and we show that thequasiparticle vertex does diverge in the spin channel, wherein the irreduciblevertex does not diverge. This divergence occurs at the Mott transition whereinthe Fermi liquid theory breaks down. Both Hubbard and Anderson lattices areinvestigated. In general, our results support that the divergences of theirreducible vertex function do not indicate a non-physical failure of theperturbation theory. Instead, the divergences are the mathematical consequenceof inverting a matrix (the local charge susceptibility) which accumulatesincreasingly negative diagonal elements as the Hubbard interaction suppressescharge fluctuations. Indeed, we find that the first symmetric divergences ofthe irreducible vertex in both Hubbard and Anderson lattices occurs near themaximum magnitude of the (negative) vertex-connected part of the chargesusceptibility, which suppresses charge fluctuations.

Fermi liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice