Coulomb- and exchange-driven redistribution of spectral correlations
Electronic correlations reorganize not only the energies of individual electronic states but also the collective structure of the spectrum. Here, first-principles density functional theory calculations combined with random-matrix spectral statistics are used to examine this reorganization in gamma-Ce within a static spin-polarized DFT+U+SOC description. We distinguish the effects of the Coulomb interaction U from those of the exchange interaction J by analyzing nearest-neighbor spacings, reduced spacing ratios, band velocities, and band curvatures across the Ce-4f manifold. Increasing U does not produce a monotonic transition between Poisson- and Wigner-Dyson-like statistics; instead, the region of strongest level repulsion migrates across the 4f manifold as the interaction increases. Exchange produces a qualitatively different response. At fixed U, strongly repulsive and strongly clustered spectral regions coexist within the same 4f manifold even while the total spin moment and 4f occupation remain nearly unchanged. The clustering persists after resolving the spectrum into its dominant j = 5/2 and j = 7/2 components and differs strongly between calculations having the same numerical value of U-J. Within the present DFT+U+SOC description, the spectral response therefore depends on the separate Coulomb and exchange interactions and cannot be represented completely by a single effective U-J parameter. These results show that energy- and character-resolved spectral statistics expose correlation-driven electronic reorganization that is hidden by conventional integrated observables.