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We evaluate the one-particle and double-occupied Green functions for theHubbard model at half-filling using the moment approach of Nolting. Ourstarting point is a self-energy, $\Sigma(\vec{k},\omega)$, which has a singlepole, $\Omega(\vec{k})$, with {\it spectral} weight, $\alpha(\vec{k})$, andquasi-particle lifetime, $\gamma(\vec{k})$. In our approach,$\Sigma(\vec{k},\omega)$ becomes the central feature of the many-body problemand due to three unkown $\vec{k}$-parameters we have to satisfy only the firstthree sum rules instead of four as in the canonical formulation of Nolting.This self-energy choice forces our system to be a non-Fermi liquid for anyvalue of the interaction, since it does not vanish at zero frequency. Theone-particle Green function, $G(\vec{k},\omega)$, shows the finger-print of astrongly correlated system, i.e., a double peak structure in the one-particlespectral density, $A(\vec{k},\omega)$, vs $\omega$ for intermediate values ofthe interaction. Close to the Mott Insulator-Transition, $A(\vec{k},\omega)$,becomes a wide single peak, signaling the absence of quasi-particles.Comment: 08 pages, 12 figures ps, revtex, submitted to Phys. Rev.

physical review. b, condensed matter

Evolution of one-particle and double-occupied Green functions for the Hubbard model, with interaction, at half-filling with lifetime effects within the moment approach