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The localized-itinerant nature of Ce-4$f$ valence electrons in heavy fermioncompound CeIn$_{3}$ under pressure is studied thoroughly by means of thecombination of density functional theory and single-site dynamical mean-fieldtheory. The detailed evolutions of electronic structures of CeIn$_{3}$,including total and partial density of states, momentum-resolved spectralfunctions, and valence state histograms etc., are calculated in a wide pressurerange where the corresponding volume compression $V/V_0 \in [0.6,1.0]$ (here$V_0$ is the experimental crystal volume) at $T \cong 116$ K. Upon increasingpressure, two strong peaks associated with the Ce-$4f$ states emerge near theFermi level, and the $c$-$f$ hybridization and valence state fluctuation areenhanced remarkably. Moreover, the kinetic and potential energies raise, whilethe occupancy, total angular momentum, and low-energy scattering rate of theCe-$4f$ electrons decline with respect to pressure. All the physicalobservables considered here exhibit prominent kinks or fluctuations in $V/V_0\in [0.80,0.90]$, which are probably the desired fingerprints for the Ce-4$f$localized-itinerant crossover.

Pressure-driven 4$f$ localized-itinerant crossover in heavy fermion compound CeIn$_{3}$: A first-principles many-body perspective