The electronic and optical properties of matter (for example, a metal, semiconductor, or more complex man-made nanostructures) are governed by the quantum-mechanical motion of the electrons inside the material. Since electrons have a negative charge, they repel each other strongly, and their motion becomes correlated as they swerve to avoid one another. The purpose of many-body theory is to describe and understand this correlation using fundamental quantum mechanics, and hence obtain an understanding of the role of correlation in the properties of the material.
Traditionally, many-body theories have been formulated for simple models that are believed to encapsulate the relevant physics of a particular phenomenon. Now, however, it is possible to combine advances in computer hardware and algorithms with the ideas of many-body theory to create a many-body theory that does not rely on the correct guessing of the physics at the start of the calculation: the basic equations of quantum mechanics are solved from first principles on powerful computers, using controllable approximations rather than ad hoc models. The physical picture emerges from analysis of the calculation.
Early applications included quasiparticle energies of semiconductors , the electronic properties of a small metallic cluster  and a metal surface . Other studies include understanding the changing nature of the electronic self-energy operator (a kind of dynamic, non-local potential that represents the effect of the electronic correlation on the motion of each individual electron) in systems where electronic correlation is stronger , and the calculation of accurate ground-state total energies for systems of interacting electrons .
1. "Accurate exchange-correlation potential for silicon and its discontinuity on addition of an electron", R.W. Godby, M. Schlüter and L.J. Sham, Physical Review Letters 56 2415 (1986). Abstract 2. "Ab initio calculations of the quasiparticle and absorption spectra of clusters: the sodium tetrameter", G. Onida, L. Reining, R.W. Godby, R. Del Sole and W. Andreoni, Physical Review Letters 75 818 (1995). Abstract 3. "Dynamic image potential at an Al(111) surface", I.D. White, R.W. Godby, M.M. Rieger and R.J. Needs, Physical Review Letters 80 4265-4268 (1998). Abstract 4. "Systematic vertex corrections through iterative solution of Hedin's equations beyond the GW approximation", A. Schindlmayr and R.W. Godby, Physical Review Letters 80 1702 (1998). Abstract 5. "Many-body GW calculations of ground-state properties: quasi-2D electron systems and van der Waals forces", P. García-González and R.W. Godby, Physical Review Letters 88 056406 (2002) [4 pages]. Abstract
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