  We study the microscopic mechanism controlling the interplay between local
charge and local spin fluctuations in correlated electron systems via a
thorough investigation of the generalized on-site charge susceptibility of
several fundamental many-electron models, such as the Hubbard atom, the
Anderson impurity model, and the Hubbard model. By decomposing the numerically
determined generalized susceptibility in terms of physically transparent
single-boson exchange processes, we unveil the microscopic mechanisms
responsible for the breakdown of the self-consistent many-electron perturbation
expansion. In particular, we unambiguously identify the origin of the
significant suppression of its diagonal entries in (Matsubara) frequency space
and the slight increase of the off-diagonal ones which cause the breakdown. The
suppression effect on the diagonal elements originates directly from the
electronic scattering on local magnetic moments, reflecting their increasingly
longer lifetime as well as their enhanced effective coupling with the
electrons. Instead, the slight and diffuse enhancement of the off-diagonal
terms can be mostly ascribed to multiboson scattering processes. The strong
intertwining between spin and charge sectors is partly weakened at the Kondo
temperature due to a progressive reduction of the effective spin-fermion
coupling of local magnetic fluctuations in the low frequency regime. Our
analysis, thus, clarifies the precise mechanism through which the physical
information is transferred between different scattering channels of interacting
electron problems and highlights the pivotal role played by such an
intertwining in the physics of correlated electrons beyond the perturbative
regime.
