  We identify the precise hallmarks of the local magnetic moment formation and
its Kondo screening in the frequency structure of the generalized charge
susceptibility. The sharpness of our identification even pinpoints an
alternative criterion to determine the Kondo temperature of strongly correlated
systems on the two-particle level, which only requires calculations at the
lowest Matsubara frequency. We showcase its strength by applying it to the
single impurity and the periodic Anderson model as well as to the Hubbard
model. Our results represent a significant progress for the general
understanding of quantum field theory at the two-particle level and allow for
tracing the limits of the physics captured by perturbative approaches in
correlated regimes.
