Dresden 2011 – wissenschaftliches Programm
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O: Fachverband Oberflächenphysik
O 87: Focussed session: Theory and computation of electronic structure: new frontiers VII (jointly with HL, DS)
O 87.3: Vortrag
Donnerstag, 17. März 2011, 18:00–18:15, TRE Phy
Insights in the T-matrix formalism — •Pina Romaniello1,4, Friedhelm Bechstedt2,4, and Lucia Reining3,4 — 1Université Paul Sabatier, Toulouse, France — 2Friedrich-Schiller-Universitaet Jena, Jena, Germany — 3École Polytechnique, Palaiseau, France — 4European Theoretical Spectroscopy Facility
In many-body perturbation theory the self-energy Σ = GWΓ plays a key role since it contains all the many body effects of the system. The exact self-energy is not known and approximations are needed. As first approximation one can neglect the vertex Γ and obtain the GW approximation. In some cases this is not sufficient, and one needs to go beyond this approximation. In this work we elucidate the concept of T-matrix [1] and its relation with Hedin's equations [2]. Starting from the exact definition of self-energy we illustrate several aspects of the T-matrix formalism: i) which approximations to the self-energy yield the T-matrix formulation, in comparison with those that, instead, yield GW and beyond; ii) the role of the particle-particle and electron-hole contributions to the T-matrix; iii) a screened version of the T-matrix; iv) an approximate vertex that produces the same self-energy as the screened T-matrix. Tests are done on the exactly solvable Hubbard molecule [3].
[1] L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics, W. A. Benjamin, Inc. New York, (1962).
[2] L. Hedin, Phys. Rev. 139, A796 (1965).
[3] P. Romaniello, S. Guyot, and L. Reining, J. Chem. Phys. 131, 154111 (2009); P. Romaniello, F. Bechstedt, L. Reining, in preparation.