NON-FERMI-LIQUID BEHAVIOR IN THE WEAK-COUPLING APPROACH TO CORRELATEDFERMIONS

It has become easy to calculate numerically self-energy corrections in second-order perturbation theory. In order to find out its capabiliti es and limitations, we analyse the weak-coupling approach for a system of one-dimensional correlated fermions. We compare the self-energy co ntributions due to different scattering processes of left- and right-m oving particles which can be treated analytically. We find that for To monaga-Luttinger processes second-order perturbation theory gives reli able results and show how deviations from Fermi-liquid behaviour and t he separation of spin- and charge-density excitations can be detected from the numerical data. Choosing the Hubbard model as a typical examp le we present numerical results for the self-energy and the spectral d ensity. Special attention is paid to the case without particle-hole sy mmetry. The insulating behaviour at half filling is outside the scope of the weak-coupling method applied.