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Many-body interactions are essential for understanding non-linear optics and ultrafast spectroscopy of materials. Recent first principles approaches based on nonequilibrium Green’s function formalisms, such as the time-dependent adiabatic GW (TD-aGW) approach, can predict nonequilibrium dynamics of excited states including electron-hole interactions. However, the high-dimensionality of the electron-hole kernel poses significant computational challenges. Here, we develop a data-driven low-rank approximation for the electron-hole kernel, leveraging localized excitonic effects in the Hilbert space of crystalline systems to achieve significant data compression through singular value decomposition (SVD). We show that the subspace of non-zero singular values remains small even as the k-grid grows, ensuring computational tractability with extremely dense k-grids. This low-rank property enables at least 95% data compression and an order-of-magnitude speedup of TD-aGW calculations. Our approach avoids intensive training processes and eliminates time-accumulated errors, seen in previous approaches, providing a general framework for high-throughput, nonequilibrium simulation of light-driven dynamics in materials. 

Abstract 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 develop here an ab initio many-body method to study nonperturbative HHG based on the real-time propagation of the non-equilibrium Green’s function with the GW self energy. We calculate the HHG of monolayer MoS₂and obtain good agreement with experiment, including the reproduction of characteristic patterns of monotonic and nonmonotonic harmonic yield in the parallel and perpendicular responses, respectively. Here, we show that many-body effects are especially important to accurately reproduce the spectral features in the perpendicular response, which reflect a complex interplay of electron-hole interactions (or exciton effects) in tandem with the many-body renormalization and Berry curvature of the independent quasiparticle bandstructure.