Accurate prediction of carrier mobility is critical for the discovery and design of next-generation electronic materials. Despite sustained progress, state-of-the-art ab initio methods remain limited by the approximate treatment of electron-phonon interactions at the density functional theory level. Here, we demonstrate that incorporating many-body $GW$ corrections to both the electronic band structure and electron-phonon couplings when solving the ab initio Boltzmann transport equation yields a mean absolute relative error of just 11% for electron mobilities across benchmark semiconductors, including Si, GaAs, GaP, diamond, and SiC. The common practice of neglecting $GW$ corrections to the electron-phonon interaction can lead to mobility errors exceeding 50%. The present findings highlight the importance of many-body $GW$ self-energy effects in carrier transport simulations and provides fundamental insights into how many-body electron-phonon interactions govern charge transport in crystalline solids.

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• Electrical conductivity
• Boltzmann theory
• Density functional theory
• First-principles calculations
• GW method
• Many-body techniques