Modified Gw Method In Electronic Systems

A modified GW approximation to many-body systems is developed. The approximation has the same computational complexity as the traditional GW approach, but uses a different truncation scheme. This scheme neglects the high-order connected correlation functions. A covariant (preserving the Ward identities due to the charge conservation) scheme for the two-body correlators is employed, which holds the relation between the charge correlator and the charge susceptibility. The method is tested on the two-dimensional one-band Hubbard model. The results are compared with exact diagonalization, the GW approximation, the fluctuation-exchange (FLEX) theory, and determinantal Monte Carlo approach. The comparison for the (one-body) Green's function demonstrates that it is more precise in the strong-coupling regime (especially away from half filling) than the GW and FLEX approximations, which have a similar complexity. More importantly, this method indicates a Mott-Hubbard gap as the Hubbard U increases, whereas the GW and FLEX methods fail. In addition, the charge correlator obtained from the covariant scheme not only holds the consistency of the static charge susceptibility, but also makes a significant improvement over the random phase approximation calculations.