Many-body perturbation theory for moiré systems

Moir\'e materials exhibit a rich spectrum of correlated phases, most notably superconductivity and insulating behavior driven by interactions. Existing theories often rely on mean-field approximations, which miss important correlation effects. Here, the authors build a many-body perturbation theory tailored to moir\'e systems, using Green's functions to go beyond mean-field. Their approach captures symmetry-breaking states, finite-temperature transitions, and self-consistent corrections to electronic properties. This framework opens a new route to better understand how interactions shape the rich physics of moir\'e materials.