Temperature-Dependent Susceptibility of the Symmetric Anderson Model: Connection to the Kondo Model

The temperature-dependent impurity susceptibility for the symmetric Anderson Hamiltonian is discussed for all physically relevant values of its parameters $U$ (the Coulomb correlation energy) and $\Gamma$ (the $d$-level width). For $U>\mathrm{}\pi \Gamma$, the results, for temperatures less than $\frac{U}{10k_B}$, map onto those of the spin-½ Kondo Hamiltonian with an effective exchange constant given by $\rho J_{\mathrm{eff}}=-\frac{8\Gamma }{\pi U}$. At higher temperatures the results show the formation of the local moment from the free orbital.