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Many-Body Perturbation Theory: The GW Approximation

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Christoph Friedrich and Arno Schindlmayr, Many-Body Perturbation Theory: The GW Approximation

Computational Nanoscience: Do It Yourself!, J. Grotendorst, S. Blugel, D. Marx (Eds.), John von Neumann Institute for Computing, Julich, NIC Series, Vol. 31, pp. 335-355, 2006

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 GW 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 GW 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.

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