# Breakdown of traditional many-body theories for correlated electrons

## TL;DR

This paper reveals that the traditional mapping from interacting to noninteracting Green's functions in many-body theories is not unique, leading to significant implications for diagrammatic approaches in strongly correlated electron systems.

## Contribution

It demonstrates the violation of the unique $G o G_0$ mapping and links this to divergences in diagrammatic expansions, highlighting non-perturbative phenomena in correlated electrons.

## Key findings

- Multiple $G_0$ can produce the same physical $G$
- Divergences in irreducible vertex diagrams are linked to non-uniqueness
- Suppression of charge susceptibility relates to non-perturbative effects

## Abstract

Starting from the (Hubbard) model of an atom, we demonstrate that the uniqueness of the mapping from the interacting to the noninteracting Green's function, $G\to G_0$, 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.