Kilian FRABOULET : Competing orders in many-electron systems: A renormalization group perspective

Kilian FRABOULET, Max Planck Institute for Solid State Research, Stuttgart

Le 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 functional renormalization group (FRG). In particular, the FRG constitutes a flexible and unbiased tool for the study of competing orders.
     I will outline recent progress in this direction for correlated electron systems. For this, I will first discuss the competition between antiferromagnetism, charge density waves and superconductivity in the 2D Hubbard model, thus making a connection with cuprate superconductors. The relation between FRG and well-known techniques (RPA, GW approximation, parquet equations, density functional theory) and 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 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 also highlight recent FRG studies of quantum criticality in Dirac materials, with a connection to graphene.