We study the influence of many-body Coulomb interactions on higher-order harmonic generation (HHG) in bulk crystals. While these carrier-carrier interactions are traditionally believed to be less important for HHG in three-dimensional materials than in two-dimensional systems, quantitative characterization of their specific role in shaping the HHG spectrum is so far lacking. In this simulation-based study, we compare the HHG spectra with and without the inclusion of the carrier-carrier interactions at the Hartree-Fock level. Simulations performed under varying excitation conditions demonstrate that the Coulomb-related effects clearly show up in the high-harmonic spectra, significantly enhancing or suppressing different harmonic bands. We also demonstrate an algorithm to accelerate numerical calculation of the Coulomb interactions, which reduces the overall computational complexity of HHG simulations at the Hartree-Fock level.

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• High-order harmonic generation
• Light-matter interaction
• Nonlinear optics
• Ultrafast phenomena