  We analyze the single-channel Kondo model using the recently developed
unitary renormalization group (URG) method, and obtain a comprehensive
understanding of the Kondo screening cloud. The fixed-point low-energy
Hamiltonian enables the computation of a plethora of thermodynamic quantities
(specific heat, susceptibility, Wilson ratio, etc.) as well as spectral
functions, all of which are found to be in excellent agreement with known
results. By integrating out the impurity, we obtain an effective Hamiltonian
for the excitations of the electrons comprising the Kondo cloud. This is found
to contain both k-space number-diagonal (Fermi liquid) as well off-diagonal
four-fermion scattering terms. Our conclusions are reinforced by a URG study of
the two-particle entanglement and many-body correlations among members of the
Kondo cloud and impurity. The entanglement between the impurity and a cloud
electron, as well as between any two cloud electrons, is found to increase
under flow towards the singlet ground state at the strong-coupling fixed point.
Both the number-diagonal and off-diagonal correlations within the conduction
cloud are also found to increase as the impurity is screened under the flow,
and the latter are found to be responsible for the macroscopic entanglement of
the Kondo-singlet ground state. The unitary RG flow enables an analytic
computation of the phase shifts suffered by the conduction electrons at the
strong-coupling fixed point. This reveals an orthogonality catastrophe between
the local moment and strong-coupling ground states, and is related to a change
in the Luttinger volume of the conduction bath. Our results offer fresh insight
on the nature of the emergent many-particle entanglement within the Kondo
cloud, and pave the way for further investigations in more exotic contexts such
as the fixed point of the over-screened multi-channel Kondo problem.
