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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 interactionstrength $U$, and the local hybridization $V$. We compare Gutzwillervariational and magnetic Hartree-Fock results in the thermodynamic limit withnumerically exact data from the Density-Matrix Renormalization Group (DMRG)method on large rings. To improve the DMRG performance, we use a canonicaltransformation to map the SIAM onto a chain with half the system size and openboundary conditions. We compare to Bethe-Ansatz results for the ground-stateenergy, magnetization, and spin susceptibility that become exact in thewide-band limit. Our detailed comparison shows that the field-theoreticaldescription 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 forintermediate and strong interactions. However, it lacks spin fluctuations andthus cannot screen the impurity spin. The Gutzwiller variational energy boundbecomes very poor for large interactions because it does not describe properlythe charge fluctuations. Nevertheless, the Gutzwiller approach provides aqualitatively correct description of the zero-field susceptibility and theKondo screening cloud. The DMRG provides excellent data for the ground-stateenergy and the magnetization for finite external fields. At stronginteractions, finite-size effects make it extremely difficult to recover theexponentially large zero-field susceptibility and the mesoscopically largeKondo screening cloud.

physical review. b./physical review. b

Ground-state properties of the symmetric single-impurity Anderson model  on a ring from Density-Matrix Renormalization Group, Hartree-Fock, and  Gutzwiller theory