Two-particle picture and electronic structure calculations Page: 4 of 22
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ments of interacting quantum systems. Instead of building the self-energy from indi-
vidual contributions to the interaction of a particle with the rest of the system, e g ,
summations of selected diagrams, we treat the entire system of N interacting three-
dimensional particles as a single particle in a configurational space of 3N dimensions.
In the non-relativistic limit considered here, the external potentials acting on the
particles as well as their mutual interactions appear as a time-independent externally
applied field Consequently, the Green function of the system can be expressed in the
familial form obtained in the traditional single-particle picture It is shown that from
a knowledge of the Green function describing n interacting particles (in an N-particle
system, with N being either finite or infinite) Green functions for m interacting par-
ticles, m < n, can be obtained directly Inveiting the resulting m-particle Green
function leads directly to the self-enrgy of the m-particle unit, extending the concept
of self-energy to an m-particle quantity. It is also shown that the solution of the
equation of motion for the many-particle Green function leads to an alternative form
for this quantity The two forms are compared and contrasted in the final discussion
Furthermore, the formulation in terms of t-matrices for both kinds of Green functions
given below provides a particularly flexible framework for the development of approx-
imate computational schemes for evaluating Green functions and the corresponding
self-energies
Another aim of the discussion is to indicate certain formal connections between
canonical many-body theory and band theory, the methodology used in the study of
the electronic structure of matter, and properties related to it Band theory is cur-
rently being implemented within the context of the local (spin) density approximation
(L(S)DA) of density functional theory (DFT)[3]. The DFT-LDA approach has been
very successful in the treatment of metallic solids[4], but is often criticized for its
approximate treatment of correlation effects It is known to provide a poor desription
of the gap in the single-particle spectrum of semiconductors and insulators, either
understimating the gap, or missing it altogether, predicting metallic behavior It also
fails to describe the volume collapse that accompanies increased pressure in many
elemental solids of the Lanthanide and Actinide series. Possibly most important is
the lack of a well-defined procedure for extending the DFT-LDA approach to alleviate
these shortcomings
It is shown below that it is possible to view DFT-LDA and canonical many-
body theory from a single perspective as two parts of a coherent whole As such,
it affords a unique, formally exact procedure for improvement, and provides a single
parameter, namely the number of particles treated explicitly, as a parameter governing
the convergence to exact results.
The following discussion is confined to the non-relativistic limit so that the inter-2
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Gonis, A; Schulthess, T C & Turchi, P E A. Two-particle picture and electronic structure calculations, article, June 24, 1998; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc671398/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.