Background
The GW approximation has become an indispensable tool for ab
initio electronic-structure calculations, because it allows an accurate
quantitative determination of excited states in solids that cannot be
matched by variational ground-state schemes like static
density-functional theory or quantum Monte Carlo. It is therefore
regarded as a reference method against which other computational schemes
must be judged. Although the GW approximation itself is only
applicable to single-particle spectra, generalisations like the
Bethe-Salpeter equation have also been successfully used to study
optical properties and collective excitations, such as excitons in
semiconductors. In addition, increasingly powerful computing facilities
have now made it possible to study complex nanostructured materials,
opening exciting perspectives for applications in nanoscience.
Building on earlier Green-function techniques, the GW
approximation was introduced by Lars Hedin in 1965 and initially applied
to the homogeneous electron gas. The accurate prediction of the
quasiparticle band structure immediately sparked a series of papers
examining other aspects of the single-particle spectrum, indicating the
potential power of this new approach. However, it took twenty years
until numerical calculations for real solids became feasible in 1985,
when first-principles band gaps for silicon and diamond were reported in
excellent agreement with experiments. Since then the GW
approximation has flourished: besides band structures, it has been used
to obtain quasiparticle lifetimes, photoemission spectra and even total
energies for a wide range of materials. Other studies have illuminated
the theoretical foundations and led to further extensions, for instance
into the strongly correlated regime. Now, another twenty years later, it
is time to assess the present achievements and examine the perspectives
for future developments. In particular, the topics of this seminar
include basic problems like the interrelation of self-consistency and
vertex corrections, novel applications to complex materials, the
relation to other electronic-structure methods as well as computational
implementation strategies.
This seminar is part of an annual workshop series on electronic
excitations organised by members of the European Network of Excellence
NANOQUANTA. Recent meetings in this series focused on  Ab initio Theoretical Approaches to the
Electronic Structure and Optical Spectra of Materials (Lyon, 2002), Ab initio Electrons Excitations Theory:
Towards Systems of Biological Interest (San Sebastian, 2003) and Theory and Modeling of Electronic Excitations
in Nanoscience (Acquafredda di Maratea, 2004).
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