Finite-temperature spectral density for the Anderson model

Spectral density of local single-particle excitations for the nondegenerate single-impurity Anderson model is calculated for various values of U/{π}{Δ}, nf⁰{≡}nf(T=0), and T, using the finite-T perturbation theory with U/{π}{Δ} as the expansion parameter and the Hartree-Fock (HF) approximation for the unperturbed Hamiltonian. For strong Coulomb correlation and at T=0, ρf({ω}) is triple peaked in the Kondo region (nf⁰{}1), double peaked in the intermediate-valence region (0.8{}nf⁰{}0.5) and single peaked in the region of nearly empty (or full) orbital. As T increases, ρf({ω}) goes through various regimes, to end up with two peaks of half-width {~}{Δ} at the single-particle excitation energies εf and εf+U. Thus the only effect of hybridization (Vkf) at high T and U{}{Δ} is the lifetime broadening of two sharp resonances obtained for Vkf{≡}0, all other many-body effects having been washed out. Comparison with finite-T HF results shows that the HF approximation is reasonable (i.e., correlation is weak) for U{}{π}{Δ} sin²(1/2{π}nf⁰) at low T, but only for U{}{Δ} at high T.