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Résumé |
The renormalization group is an established approach to study quantum many-body systems, and this applies especially to one of its modern implementations known as the functional renormalization group (FRG). In particular, the FRG constitutes a flexible and unbiased tool for the study of competing orders. In this talk, I will outline recent progress in this direction for correlated electron systems. To this end, I will first discuss the competition between antiferromagnetism, charge density waves and superconductivity in the 2D Hubbard model, thus making a connection with high-temperature superconductors. The special role of bosonization methods will be emphasized along the way. I will also show how the FRG can be combined with dynamical mean-field theory to treat strongly interacting regimes, with a focus on d-wave superconductivity. As a next step, I will increase the complexity of the model by including non-local interactions and discuss unconventional superconductivity in an extended Hubbard model with a connection to moiré materials. Special consideration will also be given to the treatment of retarded interactions with electron-phonon couplings. Finally, I will highlight recent FRG studies of quantum criticality in Dirac materials, with a connection to graphene. |
