  Quantum simulations of photoexcited low-dimensional systems are pivotal for
understanding how to functionalize and integrate novel two-dimensional (2D)
materials in next-generation optoelectronic devices. First principles
predictions are extremely challenging due to the simultaneous interplay of
light-matter, electron-electron and electron-nuclear interactions. We here
present an advanced ab initio many-body method which accounts for quantum
coherence and non-Markovian effects while treating electrons and nuclei on
equal footing, thereby preserving fundamental conservation laws like the total
energy. The impact of this advancement is demonstrated through real-time
simulations of the complex multivalley dynamics in a molybdenum disulfide
(MoS$_{2}$) monolayer pumped above gap. Within a single framework we provide a
parameter-free description of the coherent-to-incoherent crossover, elucidating
the role of microscopic and collective excitations in the dephasing and
thermalization processes.
