Moment-conserving decoupling approach for many-body systems

A nonperturbative, controllable, and moment-conserving decoupling approach is proposed. Out assumption is that a higher-order Green function (GF) essentially contains two-part information. One part relates to the single-particle GF, which is involved in the corresponding moment; the other part is a higher-order quantity, which is independent of the single-particle GF. Thus the higher-order GF may be separated into two corresponding terms. We derive the chain of equations of motion (EOM) of the latter term from the usual EOM for GF's. To solve the equations a truncation approximation is made at the level desired. The single-band Hubbard model is studied using this approach. Moment-conserving solutions up to the order m=2 are obtained. The properties of a solution corresponding to the Hubbard-I approximation level are discussed in detail. The quasiparticle bands and the momentum distribution are in excellent agreement with the results from the quantum Monte Carlo simulation. [S0163-1829(99)13747-0].