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

We evaluate the one-particle and double-occupied Green functions for the Hu bbard model at half-filling using the moment approach of Nolting [Z. Phys. 255, 25 (1972); Grund Kurs: Theoretische Physik. 7 Viel-Teilchen-Theorie (V erlag Zimmermann-Neufang, Ulmen, 1992)]. Our starting point is a self-energ y, Sigma((k) over right arrow,omega), which has a single pole, Omega((k) ov er right arrow), with spectral weight, alpha((k) over right arrow), and qua siparticle lifetime, gamma((k) over right arrow) [J. J. Rodriguez-Nunez and S. Schafroth, J. Phys. Condens. Matter 10, L391 (1998); J. J. Rodriguez-Nu nez, S. Schafroth, and H. Beck, Physica B (to be published); (unpublished)] . In our approach, Sigma((k) over right arrow,omega) becomes the central fe ature of the many-body problem and due to three unknown (k) over right arro w parameters we have to satisfy only the first three sum rules instead of f our as in the canonical formulation of Nolting [Z. Phys. 255, 25 (1972); Gr und Kurs: Theoretische Physik. 7 Viel-Teilchen-Theorie (Verlag Zimmermann-N eufang, Ulmen, 1992)]. This self-energy choice forces our system to be a no n-Fermi liquid for any value of the interaction, since it does not vanish a t zero frequency. The one-particle Green function, G((k) over right arrow,w ), shows the fingerprint of a strongly correlated system, i.e., a double pe ak structure in the one-particle spectral density, A(k,w), vs w for interme diate values of the interaction. Close to the Mott insulator-transition, A( k,w) becomes a wide single peak, signaling the absence of quasiparticles. S imilar behavior is observed for the real and imaginary parts of the self-en ergy, Sigma((k) over right arrow,omega). The double-occupied Green function , G(2)((q) over right arrow,omega), has been obtained from G((k) over right arrow,omega) by means of the equation of motion. The relation between G(2) ((q) over right arrow,omega) and the self-energy, Sigma((k) over right arro w,omega), is formally established and numerical results for the spectral fu nction of G(2)((k) over right arrow,omega), chi((2))((k) over right arrow,o mega) equivalent to - (1/pi) lims(delta-->0)+Im[G(2)((k) over right arrow,o mega)], are given. Our approach represents the simplest way to include (1) Lifetime effects in the moment approach of Nolting, as shown in the paper, and (2) Fermi or/and marginal Fermi Liquid features as we discuss in the co nclusions. [S0163-1829(99)03528-6].