Superconductivity in the Attractive Hubbard Model: The Double Hubbard--I Approximation (original) (raw)

1998, arXiv (Cornell University)

Using the Dyson equation of motion for both the diagonal one-particle Green function, G(k, ω) and off-diagonal Green function, F (k, ω), at the level of the Hubbard-I decoupling scheme, we have found that they have four poles symmetric in pairs, justifying a more elaborated calculation done by the Zürich group by means of the T-Matrix approach (Pedersen et al, Z. Physik B 103, 21 (1997)) and the moment approach of Nolting (Z. Physik 255, 25 (1972)). We find that the energy spectra and the weights of G(k, ω) and F (k, ω) have to be calculated self-consistently. G(k, ω) satisfies the first two moments while F (k, ω) the first sum rule. Our order parameter α(T) is given by 1/Ns k ε(k)∆(k). Due to the fact that we have a purely local attractive interaction ∆(k) can be of any s-type wave. However, for a pure s-wave, for which α(T) = 0, we go back to the mean-field BCS results, with a renormalized chemical potential. In this case, the off-diagonal Green function, F (k, ω), satisfies the first two off-diagonal sum rules. We explicitly state the range of validity of our approximation.