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Many-body effects play an important role in enhancing and modifying optical absorption and other excited-state properties of solids in the perturbative regime, but their role in high harmonic generation (HHG) and other nonlinear response beyond the perturbative regime is not well-understood.

We present here an ab initio many-body method based on the real-time propagation of the non-equilibrium Green’s function with the GW self energy to the study of nonperturbative HHG. We calculate the HHG of monolayer MoS2 and obtain excellent agreement with experiment, including the reproduction of patterns of monotonic and nonmonotonic harmonic yield in the parallel and perpendicular responses, respectively. We find that many-body effects are essential to reproducing these spectral features, which represent the complex interplay of electron-hole interactions (or exciton effects) in tandem with the many-body renormalization of the independent quasiparticle bandstructure.