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The Interacting Electron Gas

Henrik Bruus, Karsten Flensberg

Published Sep 2, 2004• 1 citation
Publisher

Abstract

Abstract In this chapter, we reanalyze the Coulomb-interacting electron gas in the jellium model using the Feynman diagram technique, and we show how a meaningful finite groundstate energy can be found.
DOI
10.1093/oso/9780198566335.003.0014

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At the end of the last chapter, we considered the electron-electron interaction. Here, we found two terms: the Hartree energy and the exchange energy. These work fine if we can solve for the energy exactly. However, as was remarked, this can only be done for a few electron systems. For more meaningful systems, we need to develop an approximation technique for the interacting Green’s functions. The standard approach to this is via the interaction representation, which gives us a prescription for developing the perturbation series. As one might infer from our previous discussion, this will lead to multiple, messy integrals. Fortunately, the Feynman diagrams give us an elegant and pictorial method of looking at the various terms in the perturbation series. As a result, they also give us a much more intuitive method of examining the various terms.
Precise calculations of dynamics in the homogeneous electron gas (jellium model) are of fundamental importance for design and characterization of new materials. We introduce a diagrammatic Monte Carlo technique based on algorithmic Matsubara integration that allows us to compute frequency and momentum resolved finite temperature response directly in the real frequency domain using a series of connected Feynman diagrams. The data for charge response at moderate electron density are used to extract the frequency dependence of the exchange-correlation kernel at finite momenta and temperature. These results are as important for development of the time-dependent density functional theory for materials dynamics as ground state energies are for the density functional theory.