Many-body perturbation theory: The GW approximation

C. Friedrich, A. Schindlmayr, in: J. Grotendorst, S. Blügel, D. Marx (Eds.), Computational Nanoscience: Do It Yourself!, John von Neumann Institute for Computing, Jülich, 2006, pp. 335–355.

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Abstract
In this lecture we present many-body perturbation theory as a method to determine quasiparticle excitations in solids, especially electronic band structures, accurately from first principles. The main ingredient is the electronic self-energy that, in principle, contains all many-body exchange and correlation effects beyond the Hartree potential. As its exact mathematical expression is unknown, approximations must be used in practical calculations. The approximation is obtained using a systematic algebraic approach on the basis of Green function techniques. It constitutes an expansion of the self-energy up to linear order in the screened Coulomb potential, which describes the interaction between the quasiparticles and includes dynamic screening through the creation of exchange-correlation holes around the bare particles. The implementation of the approximation relies on a perturbative treatment starting from density functional theory. Besides a detailed mathematical discussion we focus on the underlying physical concepts and show some illustrative applications.
Publishing Year
Book Title
Computational Nanoscience: Do It Yourself!
Volume
31
Page
335-355
Conference
NIC Winter School
Conference Location
Jülich
Conference Date
2006-02-14 – 2006-02-22
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Friedrich C, Schindlmayr A. Many-body perturbation theory: The GW approximation. In: Grotendorst J, Blügel S, Marx D, eds. Computational Nanoscience: Do It Yourself!. Vol 31. NIC Series. Jülich: John von Neumann Institute for Computing; 2006:335-355.
Friedrich, C., & Schindlmayr, A. (2006). Many-body perturbation theory: The GW approximation. In J. Grotendorst, S. Blügel, & D. Marx (Eds.), Computational Nanoscience: Do It Yourself! (Vol. 31, pp. 335–355). Jülich: John von Neumann Institute for Computing.
@inbook{Friedrich_Schindlmayr_2006, place={Jülich}, series={NIC Series}, title={Many-body perturbation theory: The GW approximation}, volume={31}, booktitle={Computational Nanoscience: Do It Yourself!}, publisher={John von Neumann Institute for Computing}, author={Friedrich, Christoph and Schindlmayr, Arno}, editor={Grotendorst, Johannes and Blügel, Stefan and Marx, DominikEditors}, year={2006}, pages={335–355}, collection={NIC Series} }
Friedrich, Christoph, and Arno Schindlmayr. “Many-Body Perturbation Theory: The GW Approximation.” In Computational Nanoscience: Do It Yourself!, edited by Johannes Grotendorst, Stefan Blügel, and Dominik Marx, 31:335–55. NIC Series. Jülich: John von Neumann Institute for Computing, 2006.
C. Friedrich and A. Schindlmayr, “Many-body perturbation theory: The GW approximation,” in Computational Nanoscience: Do It Yourself!, vol. 31, J. Grotendorst, S. Blügel, and D. Marx, Eds. Jülich: John von Neumann Institute for Computing, 2006, pp. 335–355.
Friedrich, Christoph, and Arno Schindlmayr. “Many-Body Perturbation Theory: The GW Approximation.” Computational Nanoscience: Do It Yourself!, edited by Johannes Grotendorst et al., vol. 31, John von Neumann Institute for Computing, 2006, pp. 335–55.
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