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Evolution of One-Particle and Double-Occupied Green Functions for the Hubbard Model at Half-Filling With Lifetime Effects Within The Moment Approach

We evaluate the one-particle and double-occupied Green functions for the Hubbard model at half-filling using the moment approach of Nolting. Our starting point is a self-energy, $Σ(\vec{k},ω)$, which has a single pole, $Ω(\vec{k})$, with {\it spectral} weight, $α(\vec{k})$, and quasi-particle lifetime, $γ(\vec{k})$. In our approach, $Σ(\vec{k},ω)$ becomes the central feature of the many-body problem and due to three unkown $\vec{k}$-parameters we have to satisfy only the first three 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 any value of the interaction, since it does not vanish at zero frequency. The one-particle Green function, $G(\vec{k},ω)$, shows the finger-print of a strongly correlated system, i.e., a double peak structure in the one-particle spectral density, $A(\vec{k},ω)$, vs $ω$ for intermediate values of the interaction. Close to the Mott Insulator-Transition, $A(\vec{k},ω)$, becomes a wide single peak, signaling the absence of quasi-particles.