THE 2ND-ORDER U-PERTURBATION APPROACH TO THE ANDERSON LATTICE MODEL IN ONE, 2 AND 3 DIMENSIONS

The second order (standard) U-perturbation treatment around the non-magnetic Hartree-Fock solution of the periodic Anderson model may already provide for a proper approximation for the description of heavy fermion systems. Unfortunately for low dimensions d the practical computation of the full momentum (k-)dependent f-electron selfenergy usually is extremely difficult within this approach, as a 2d-fold momentum integration over a singular integrand is required. Therefore, until recently most applications were restricted to d=1. Recently we have shown that these calculations are greatly simplified when studying the model in the limit d→∞, as the local approximation is correct for d=∞, i.e. the selfenergy is site-diagonal (momentum-independent). In this communication we show that this limit d→∞ can even be used to determine the full k-dependent selfenergy for low dimensions d(=1,2,3) much more efficiently than before. Starting from the local approximation for a finite d we take into account the corrections by considering the nearest neighbor, next nearest neighbor, etc. contributions to the selfenergy; this corresponds to a 1 d-expansion, which converges even for d=1. We present results for the momentum and frequency dependence of the f-electron selfenergy and the energy dependence of the f-electron spectral function for d=1,2,3. The 1 d corrections become less and less important with increasing d, and d=∞ (i.e. the local approximation) provides already for a good description of three dimensional systems. © 1990.