System Green functions for interacting quantum particles

Abstract

We propose a formalism for the study of many-particle interacting quantum systems that allows the determination of the Green function of the system as a whole and corresponding Green functions of lower order from a knowledge of any Green function of a higher order. We illustrate the formalism by means of calculations on a model single-band system described by a Hamiltonian of tight-binding kind and corresponding to four electrons on a ring of four sites.

Acknowledgments

Conversations with P.E.A. Turchi, A. Caro, A. McMahan and D.M. Nicholson are hereby gratefully acknowledged. This work was performed under the auspices of the US Department of Energy by the University of California through the Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48.

Notes

†The properties, advantages and limitations of the LDA have been studied and reported extensively in the literature, as have the attempts at lifting these limitations and they will not be discussed further in the present work. The aim here is to provide a rationale for the development of procedures that account for both the presence of external fields as well as interparticle interactions on an equal formal basis.