Going beyond the cumulant approximation systematically: Power series expansion of quasiparticle Green’s function.

The cumulant expansion of quasiparticle Green’s function has been quite popular and successful in going beyond the one-electron picture and describing electronic correlation that manifest as satellite sidebands¹. However, this method is not systematically improvable and only takes into account only some fraction of interband interaction because of the truncation of Dyson series. In this work, we provide a method to systematically improve the quasiparticle Green’s function by using power series corrections and self consistently including the corrections within the self energy. This method does not truncate the Dyson series and the final correction equations are recursive in nature. We also show the derivation of time-ordered and retarded cumulant expansion results from this method and elucidate the underlying approximations on self energy in both cases. Finally, we show an application of this method on a simple two band model and compare them to cumulant results.
¹Kas et al, Phys. Rev. B 90, 085112 (2014)