Marrying the predictive power of ab initio calculations with many-body effects remains a challenging task in two-dimensional (2D) materials, where efficient carrier-carrier interaction challenges established approximation schemes. In particular, understanding exciton-phonon interaction from first principles is a field of growing interest. Here, we present a many-body theory for coupled free-carrier, exciton, phonon and photon dynamics based on carrier-carrier and carrier-phonon interaction matrix elements obtained via projection on Wannier orbitals. The framework is applied to study the impact of carrier-phonon correlations on optical spectra and coupled nonequilibrium carrier-phonon kinetics in monolayer ${\mathrm{MoSe}}_2$. We find that non-Markovian effects and dynamical buildup of quasiparticles are only properly described if correlations at least on the two-phonon level are included. Our studies open a perspective to advance the material-realistic many-body description of nonequilibrium physics in 2D nanostructures.

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• Excitons
• Phonons
• 2-dimensional systems
• Cluster expansion
• Many-body techniques
• Non-Markovian processes
• Wannier function methods