We apply correlation matrix renormalization theory (CMRT) to cerium nitride (CeN) under pressure. For $B1$ (NaCl-type) phase, CMRT gives an equation of state consistent with ambient pressure experiments. It produces electronic density-of-state (DOS) characterized by a sharp $4f$ quasiparticle resonance peak pinned at the Fermi level and two subbands formed by strong hybridization between the localized Ce-$4f$ electrons and the itinerant Ce-$5d$ and N-$2p$ electrons below the Fermi level, consistent with x-ray photoemission spectroscopy experiments. Upon compression, CMRT predicts a first-order $B1$ → $B2$ (CsCl-type) transition with $\sim 11\%$ volume collapse in agreement with experiments. Across the transition, the $4f$ spectrum broadens, the $4f$ orbital occupancy increases, and the hybridization with conduction states enhances, signaling a crossover from partially localized to more itinerant $4f$ behavior. These features are in excellent agreement with experimental observations, demonstrating that CMRT provides a parameter-free description and prediction of correlation-driven structural and electronic transitions in rare-earth compounds.

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• Density of states
• Phase transitions
• Strongly correlated systems
• Ab initio calculations