Correlated excitations across space and time: From Wigner crystalline excitons to ultrafast nonequilibrium dynamics

The past few years have seen remarkable progress in uncovering how strong correlations shape both the equilibrium and dynamical excitations of quantum materials. In this talk, I will present a unified first-principles perspective enabled by new many-body perturbation theory advances. I will first discuss how excitons arise from strongly correlated generalized Wigner-crystal ground states in transition-metal dichalcogenide moiré superlattices, using the GW-Bethe-Salpeter equation (GW-BSE) approach. Our results uncover the propagation of correlation effects from ground states to excited states, and the two-particle excitonic correlations dominate over the kinetic energy of the free electron-hole pairs. To extend to the nonequilibrium study, coupling between electronic excitations and phonons becomes critical. I will introduce recent progress in GW perturbation theory (GWPT) for correlated electron-phonon coupling, particularly demonstrating the previously overlooked self-energy effects in the long-range Fröhlich interaction. Finally, I will present our recent development of a time-dependent adiabatic GW approach with electron-phonon coupling included across the full Brillouin zone (TD-aGW-ph). TD-aGW-ph captures the nonequilibrium and coherent exciton-phonon coupled dynamics, as will be demonstrated in monolayer MoS₂ with a pump-probe angle-resolved photoemission spectroscopy setup. These results outline a comprehensive framework for correlated quantum materials from first principles.