  We study the nonequilibrium formation of a spin screening cloud that
accompanies the quenching of a local magnetic moment immersed in a Fermi sea at
zero temperature. Based on high precision density matrix renormalization group
results for the interacting single impurity Anderson model we discuss the real
time evolution after a quantum quench in the impurity-reservoir hybridization
using time evolving block decimation. We report emergent length and time scales
in the spatiotemporal structure of non-local correlation functions in the spin-
and the charge density channel. At equilibrium, our data for the correlation
functions and the extracted length-scales show good agreement with existing
results, as do local time dependent observables at the impurity. In the
time-dependent data, we identify a major signal which defines a "light cone"
moving at the Fermi velocity and a ferromagnetic component in its wake. Inside
the light cone we find that the structure of the nonequilibrium correlation
functions emerges on two time scales. Initially, the qualitative structure of
the correlation functions develops rapidly at the lattice Fermi velocity.
Subsequently the spin correlations converge to the equilibrium results on a
much larger time scale. This process sets a dynamic energy scale, which we
identify to be proportional to the Kondo temperature. Outside the light cone we
observe two different power law decays of the correlation functions in space,
with time and interaction strength independent exponents.
