Second order U-perturbation approach to the Anderson lattice model in high dimensions

Abstract

We study the periodic Anderson model (PAM), i.e. highly correlated, localized f-shells on a d-dimensional (simple-cubic) lattice hybridized with the states of a (tight-binding) conduction band. At least for the symmetric PAM (i.e. the unperturbed f-level energy E f and E f+U lie symmetric around the chemical potential, where U denotes the on-site Coulomb correlation between the f-electrons,) the second order (standard) U-perturbation treatment around the non-magnetic Hartree-Fock solution provides for a proper approximate treatment of the PAM even for relatively large values of U. In this communication we study this approach in the limit of high dimensions d of the underlying lattice. In this limit, which has recently been introduced by Metzner and Vollhardt for the Hubbard model, the selfenergy becomes site-diagonal, i.e. momentum independent, because of which the explicit calculation of the selfenergy in second order in U is much simpler than in lower dimensions. But one still obtains an f-electron spectral function, which shows all the properties, which are usually expected for heavy fermion systems, in particular single-particle peaks near to E f and E f+U, a strongly temperature dependent many-particle (Kondo) resonance peak near to the chemical potential, a hybridization (coherence) gap at the chemical potential, etc. Thus practical calculations may become much simpler for high d, but the essential physics remains the same as for realistic low d (=1,2,3).