Cumulant expansion of the retarded one-electron Green function

The cumulant expansion is a powerful approach for including correlation effects in electronic structure calculations beyond the GW approximation. However, the expansion is not generally valid, as current implementations ignore terms that mix particle and hole states and lead to partial occupation numbers of one-electron states. These limitations are corrected here using a cumulant expansion of the retarded one-electron Green's function that includes both particle and hole contributions. The approach provides a consistent framework that improves on the GW approximation to the spectral function without additional computational effort. The method is illustrated with results for the homogeneous electron gas and comparisons to experiment and other methods.