  Using the state-of-art dynamical mean-field theory combined with density
functional theory method, we have performed systematic study on the temperature
and pressure dependent electronic structure of ferromagnetic quantum critical
material candidate CeRh$_6$Ge$_4$. At -3.9 GPa and -8.3 GPa, the Ce-4$f$
occupation variation, the local magnetic susceptibility, and the low-frequency
electronic self-energy behaviors suggest the Ce-4$f$ electrons are in the
localized state; whereas at 6.5 GPa and 13.1 GPa, these quantities indicate the
Ce-4$f$ electrons are in the itinerant state. The characteristic temperatures
associated with the coherent Kondo screening is gradually suppressed to 0
around 0.8 GPa upon releasing external pressure, indicative of a local quantum
critical point. Interestingly, the momentum-resolved spectrum function shows
that even at the localized state side, highly anisotropic
$\mathbf{k}$-dependent hybridization between Ce-4$f$ and conduction electrons
is still present along $\Gamma$-A, causing hybridization gap in between. The
calculations predict 8 Fermi surface sheets at the local-moment side and 6
sheets at the Kondo coherent state. Finally, the self-energy at 0.8 GPa can be
well fitted by marginal Fermi-liquid form, giving rise to a linearly
temperature dependent resistivity.
