Self-consistent U-perturbation treatment of the Anderson lattice model in high dimensions

Abstract

To describe heavy fermion and valence fluctuating materials the periodic Anderson model (PAM) is studied on a d-dimensional simple cubic lattice in the limit of high dimensions d. In this non-trivial limit the essential physical properties remain the same as for realistic low dimensions, but the practical calculations are greatly simplified. We calculate the f-electron self-energy and spectral function self-consistently up to the second order within the standard perturbation theory with respect to the on-site Coulomb correlation U between the f-electrons. One obtains a strongly temperature dependent many-particle peak at the chemical potential within the f-electron spectral function and an f-electron self-energy, whose imaginary part vanishes at the Fermi level for zero temperature, while the real part has a strong negative slope, leading naturally to heavy quasiparticles with infinite lifetime. This is the first treatment of the PAM, which fulfills all commonly expected Fermi liquid properties and sum rules.