Relaxation processes following light excitation in semiconductors are key in materials-based quantum technology applications. These processes are broadly studied in atomically thin transition-metal dichalcogenides, quasi-two-dimensional excitonic semiconductors in which atomistic design allows for tunable excited-state properties, such as relaxation lifetimes and photoinduced coherence. In this work, we present a density-matrix-based approach to compute exciton relaxation within a many-body ab initio perspective. We expand our previously developed Lindblad density-matrix formalism to capture multichannel electron-hole pair relaxation processes, including phonon and Coulomb scattering as well as radiative recombination, and we study their effect on the time-resolved excited-state propagation. Using monolayer ${\mathrm{MoSe}}_2$ as a prototypical example, we examine many-body effects on the time-dependent dynamics of photoactive excitations, exploring how the electron-hole pair interactions are reflected in variations of the excitation energy, spectral signature, and state coherence. Our method supplies a detailed understanding of exciton relaxation mechanisms in realistic materials, offering a previously unexplored pathway to study excited-state dynamics in semiconductors from first principles.

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• Excitons
• Quantum coherence & coherence measures
• Transition metal dichalcogenides
• Band structure methods
• Bethe-Salpeter equation
• Density matrix methods
• First-principles calculations
• GW method