Finite-temperature spectral density for the Anderson model

Abstract

Spectral density of local single-particle excitations for the nondegenerate single-impurity Anderson model is calculated for various values of U/\ensuremath{\pi}\ensuremath{\Delta}, ${n}_{f}^{0}$\ensuremath{\equiv}${n}_{f}$(T=0), and T, using the finite-T perturbation theory with U/\ensuremath{\pi}\ensuremath{\Delta} as the expansion parameter and the Hartree-Fock (HF) approximation for the unperturbed Hamiltonian. For strong Coulomb correlation and at T=0, ${\ensuremath{\rho}}_{f}$(\ensuremath{\omega}) is triple peaked in the Kondo region (${n}_{f}^{0}$\ensuremath{\simeq}1), double peaked in the intermediate-valence region (0.8\ensuremath{\gtrsim}${n}_{f}^{0}$\ensuremath{\gtrsim}0.5) and single peaked in the region of nearly empty (or full) orbital. As T increases, ${\ensuremath{\rho}}_{f}$(\ensuremath{\omega}) goes through various regimes, to end up with two peaks of half-width \ensuremath{\sim}\ensuremath{\Delta} at the single-particle excitation energies ${\ensuremath{\varepsilon}}_{f}$ and ${\ensuremath{\varepsilon}}_{f}$+U. Thus the only effect of hybridization (${V}_{\mathrm{k}f}$) at high T and U\ensuremath{\gg}\ensuremath{\Delta} is the lifetime broadening of two sharp resonances obtained for ${V}_{\mathrm{k}f}$\ensuremath{\equiv}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\ensuremath{\lesssim}\ensuremath{\pi}\ensuremath{\Delta} ${\mathrm{sin}}^{2}$(1/2\ensuremath{\pi}${\mathrm{n}}_{\mathrm{f}}^{0}$) at low T, but only for U\ensuremath{\lesssim}\ensuremath{\Delta} at high T.