Evolution of One-Particle and Double-Occupied Green Functions for the Hubbard Model at Half-Filling With Lifetime Effects Within The Moment Approach
Abstract
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, (k,ω), which has a single pole, (k), with spectral weight, α(k), and quasi-particle lifetime, γ(k). In our approach, (k,ω) becomes the central feature of the many-body problem and due to three unkown 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(k,ω), shows the finger-print of a strongly correlated system, i.e., a double peak structure in the one-particle spectral density, A(k,ω), vs ω for intermediate values of the interaction. Close to the Mott Insulator-Transition, A(k,ω), becomes a wide single peak, signaling the absence of quasi-particles.
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