  We analyze the ground-state energy, magnetization, magnetic susceptibility,
and Kondo screening cloud of the symmetric single-impurity Anderson model
(SIAM) that is characterized by the band width $W$, the impurity interaction
strength $U$, and the local hybridization $V$. We compare Gutzwiller
variational and magnetic Hartree-Fock results in the thermodynamic limit with
numerically exact data from the Density-Matrix Renormalization Group (DMRG)
method on large rings. To improve the DMRG performance, we use a canonical
transformation to map the SIAM onto a chain with half the system size and open
boundary conditions. We compare to Bethe-Ansatz results for the ground-state
energy, magnetization, and spin susceptibility that become exact in the
wide-band limit. Our detailed comparison shows that the field-theoretical
description is applicable to the SIAM on a ring for a broad parameter range.
Hartree-Fock theory gives an excellent ground-state energy and local moment for
intermediate and strong interactions. However, it lacks spin fluctuations and
thus cannot screen the impurity spin. The Gutzwiller variational energy bound
becomes very poor for large interactions because it does not describe properly
the charge fluctuations. Nevertheless, the Gutzwiller approach provides a
qualitatively correct description of the zero-field susceptibility and the
Kondo screening cloud. The DMRG provides excellent data for the ground-state
energy and the magnetization for finite external fields. At strong
interactions, finite-size effects make it extremely difficult to recover the
exponentially large zero-field susceptibility and the mesoscopically large
Kondo screening cloud.
