The interplay Coulomb and electron-phonon interactions with thermal and quantum fluctuations facilitates rich phase diagrams, especially in two-dimensional electron systems. Layered transition metal dichalcogenides hosting charge, excitonic, spin and superconducting order form an epitomic material class in this respect. However, despite intensive research a realistic understanding of the competition between these quantum phases has remained essentially unresolved.

Here, we theoretically analyze the combined electronic correlation effects as resulting from simultaneous short- and long-range Coulomb as well as electron-phonon interactions in NbS₂ monolayers. Therefore, we derive highly material-realistic lattice models from first principles and solve them using a state-of-the-art many-body solver, i.e. the dual boson approach. We find an unexpected coexistence of strong charge and spin fluctuations. The fully correlated electronic spectral function resembles the non-interacting band structure but with appreciable broadening due to coupling of the electrons to collective degrees of freedom. Our findings point towards interesting prospects for quantum engineering of two-dimensional materials.