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Physical Review Letters

Difficulty in the Method of Green's Functions for a Many-Body System

Roger Balian, Lewis H. Nosanow, N. R. Werthamer

Published May 1, 1962• 16 citations
Publisher
DOI
10.1103/physrevlett.8.372

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A new approach to the two-time Green function method is proposed. In order to give a systematic way of decoupling the two-time Green functions and to overcome the difficulties often encountered in terminating the hierarchy of Green functions, a generating function is introduced and its properties are examined in detail for a simple model. It is shown that the generating function provides poweful tool even in the case where conventional approximation for Green functions does not work. An example of the generating function is constructed for Fermion system with two-body interaction.
We present results for many-body perturbation theory for the one-body Green's function at finite temperatures using the Matsubara formalism. Our method relies on the accurate representation of the single-particle states in standard Gaussian basis sets, allowing to efficiently compute, among other observables, quasiparticle energies and Dyson orbitals of atoms and molecules. In particular, we challenge the second-order treatment of the Coulomb interaction by benchmarking its accuracy for a well-established test set of small molecules, which includes also systems where the usual Hartree-Fock treatment encounters difficulties. We discuss different schemes how to extract quasiparticle properties and assess their range of applicability. With an accurate solution and compact representation, our method is an ideal starting point to study electron dynamics in time-resolved experiments by the propagation of the Kadanoff-Baym equations.