Starting from the (Hubbard) model of an atom, we demonstrate that the uniqueness of the mapping from the interacting to the noninteracting Greens function, $Gto G_0$, is strongly violated, by providing numerous explicit examples of different $G_0$ leading to the same physical $G$. We argue that there are indeed infinitely many such $G_0$, with numerous crossings with the physical solution. We show that this rich functional structure is directly related to the divergence of certain classes of (irreducible vertex) diagrams, with important consequences for traditional many-body physics based on diagrammatic expansions. Physically, we ascribe the onset of these highly non-perturbative manifestations to the progressive suppression of the charge susceptibility induced by the formation of local magnetic moments and/or RVB states in strongly correlated electron systems.
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