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mercredi 23 mars — 10:30 attention, horaire exceptionnel

Electron correlation in a Hubbard cluster

Daniel Wilkin (Friedrich-Schiller-Universität)

par Pierre Pujol - 23 mars 2011

An important method in many-particle physics is related to the Hubbard model which can be used to investigate the behavior of fermions, particularly to study exchange and correlation of electronelectron interaction we are interested in. For a special cluster, the molecule consisting of two atoms, the electrons interact via one hopping integral, and for a small number of N = 1, 2, 3 electrons the model has the advantage that it can be solved exactly. Therefore, some important physical quantities like the Green’s function, the spectral function and the self-energy are calculated and discussed. Exchange and correlation are fully treated. The self-energies obtained by two approximate methods, namely the Hartree-Fock and the GW approximation, are compared with the exact self-energy. The comparison allows a discussion of the validity of the approximations versus the ratio of Hubbard parameter and hopping integral. Finally, we evaluate the vertex function for the Hubbard molecule.