Cluster methods for strongly correlated systems / mèthodes d'amas quantiques pour les systèsmes fortement corrèlès

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A large fraction of modern technology (computers, telecommunications, electronics in general) relies on the properties of electrons in solids. Depending on the behavior of electrons, solids can be metals, insulators, magnets, semiconductors, superconductors and so on. Our theoretical understanding of electrons in solids is based on quantum mechanics, but often within a simple, approximate model in which electrons do not interact very much with each other. This simple model is at fault in many interesting materials where the effects of electron-electron repulsion are strong. We say that electrons in such materials are "strongly correlated". I study theoretical models of strongly correlated electrons in solids, in the framework of quantum mechanics and with the help of powerful computers.