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We analyze the ground-state energy, local spin correlation, impurity spinpolarization, impurity-induced magnetization, and corresponding zero-fieldsusceptibilities of the symmetric single-impurity Kondo model on atight-binding chain with bandwidth $W=2{\cal D}$ and coupling strength $J_{\rmK}$. We compare perturbative results and variational upper bounds from Yosida,Gutzwiller, and first-order Lanczos wave functions to the numerically exactdata obtained from the Density-Matrix Renormalization Group (DMRG) and from theNumerical Renormalization Group (NRG) methods. The Gutzwiller variationalapproach becomes exact in the strong-coupling limit and reproduces theground-state properties from DMRG and NRG for large couplings. We calculate theimpurity spin polarization and its susceptibility in the presence of magneticfields that are applied globally/locally to the impurity spin. The Yosida wavefunction provides qualitatively correct results in the weak-coupling limit. InDMRG, chains with about $10^3$ sites are large enough to describe thesusceptibilities down to $J_{\rm K}/{\cal D}\approx 0.5$. For smaller Kondocouplings, only the NRG provides reliable results for a general host-electrondensity of states $\rho_0(\epsilon)$. To compare with results from BetheAnsatz, we study the impurity-induced magnetization and zero-fieldsusceptibility. For small Kondo couplings, the zero-field susceptibilities atzero temperature approach $\chi_0(J_{\rm K}\ll {\cal D})/(g\mu_{\rmB})^2\approx \exp[1/(\rho_0(0)J_{\rm K})]/(2C{\cal D}\sqrt{\pi e\rho_0(0)J_{\rm K}})$, where $\ln(C)$ is the regularized first inverse momentof the density of states. Using NRG, we determine the universal sub-leadingcorrections up to second order in $\rho_0(0)J_{\rm K}$.

Symmetric single-impurity Kondo model on a tight-binding chain: a comparison of analytical and numerical ground-state approaches