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

摘要

We evaluate the one-particle and double-occupied Green functions for the Hubbard model at half-filling using the moment approach of Nolting [Z. Phys. 255, 25 (1972); Grund Kurs: Theoretische Physik. 7 Viel-Teilchen-Theorie (Verlag Zimmermann-Neufang, Ulmen, 1992)]. Our starting point is a self-energy, Sigma((k) over right arrow,omega), which has a single pole, Omega((k) over right arrow), with spectral weight, alpha((k) over right arrow), and quasiparticle lifetime, gamma((k) over right arrow) [J. J. Rodriguez-Nunez and S. Schafroth, J. Phys. Condens. Matter 10, L391 (1998); J. J. Rodriguez-Nunez, S. Schafroth, and H. Beck, Physica B (to be published); (unpublished)]. In our approach, Sigma((k) over right arrow,omega) becomes the central feature of the many-body problem and due to three unknown (k) over right arrow parameters we have to satisfy only the first three sum rules instead of four as in the canonical formulation of Nolting [Z. Phys. 255, 25 (1972); Grund Kurs: Theoretische Physik. 7 Viel-Teilchen-Theorie (Verlag Zimmermann-Neufang, Ulmen, 1992)]. 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) over right arrow,w), shows the fingerprint of a strongly correlated system, i.e., a double peak structure in the one-particle spectral density, A(k,w), vs w for intermediate values of the interaction. Close to the Mott insulator-transition, A(k,w) becomes a wide single peak, signaling the absence of quasiparticles. Similar behavior is observed for the real and imaginary parts of the self-energy, 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 arrow,omega), is formally established and numerical results for the spectral function of G(2)((k) over right arrow,omega), chi((2))((k) over right arrow,omega) equivalent to - (1/pi) lims(delta-->0)+Im[G(2)((k) over right arrow,omega)], 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 conclusions. [S0163-1829(99)03528-6]. [References: 65]