Covariant cubic approximation for many-body electronic systems

An approximation scheme determining the excitations of an electronic model on the lattice with pairwise interactions is proposed. A systematic truncation of the set of Dyson-Schwinger equations for correlators, supplemented by a "covariant" calculation of correlators lead to a converging series of approximates. The covariance preserves all the Ward identities among correlators describing various condensed matter probes. It is shown that the third-order approximant of this kind beyond classical and Gaussian (Hartree-Fock) is precise enough and due to several fortunate features the complexity of calculation is surprisingly low so that a realistic material computation might be feasible. Focus here is on the electron field correlator describing the electron (hole) excitations measured in photoemission and other probes. The scheme is tested on several solvable benchmark models.