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.

Many classes of materials are stronly correlated, but the most famous are the high-temperature superconductors, discovered in the late 1980s. Superconductivity is a strange phenomenon by which a material can, at a low-enough temperature, carry electricity without resistance and expell all magnetic fields. Superconductivity is well understood in "traditional" metallic alloys, where the phenomenon is caused by an effective mutual attraction of electrons caused by vibrations of the crystal lattice. But in high-temperature superconductors a new mechanism is needed to explain the phenomenon, and many scientists believe that the strong electric interaction of electrons, that normally would keep electrons away from each other and lead to an insulator, can paradoxically cause an effective attraction of electrons in some circumstances and cause superconductivity. One of the objectives of my research is to check whether this is indeed the case in a simple model of strongly correlated electrons: the Hubbard model. For this I use new theoretical methodology that I contribute to develop, and that brings together the power of computers with analytical (pen and paper) calculations. Other classes of materials (such as organic superconductors) can also be studied with these methods.

For a review of the methods used in my research, please see:
David Sénéchal, An introduction to quantum cluster methods, arXiv:0806.2690 (2008)