In rare-earth Weyl semimetals, the correlated $f$ electrons play a crucial role in shaping the characteristics of Weyl nodes, potentially giving rise to magnetic Weyl states or correlated Weyl excitations. In this study, we investigate a recently discovered noncentrosymmetric Weyl semimetal, $R\mathrm{GaGe}$ $(R=\text{La,}\text{Ce,}\text{Pr})$. By combining density functional theory with dynamical mean-field theory, we demonstrate that the $f$ electrons in CeGaGe and PrGaGe are nearly fully localized. Concurrently, four inequivalent types of Weyl nodes emerge in spd bands. Notably, the $W_3^{\prime }$ Weyl point exhibits a pronounced chiral separation, leading to long Fermi arcs on the (001) surface. Below the magnetic transition temperature, the $f$-magnetic moments not only create new Weyl point $W_4^{\prime }$, but they also induce displacement of other Weyl nodes, resulting in anomalous Hall conductance. $W_4^{\prime }$ and $W_3^{\prime }$ generate double Fermi arcs on the (001) surface, which remain distinctly separated from bulk states, facilitating future experimental detection. Under volume compression, the $f$ electrons in CeGaGe progressively become itinerant and begin to obscure the Weyl nodes, making them difficult to resolve within a single-particle framework. However, upon heating beyond a critical temperature, the $f$ electrons regain localization, and the Weyl state can once again be effectively described. These findings indicate that in the $R\mathrm{GaGe}$ system, temperature and pressure can be utilized to drive intriguing transitions among paramagnetic Weyl semimetals, magnetic Weyl semimetals, and correlated Weyl semimetals.

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• Kondo effect
• Spin-orbit coupling
• Surface states
• Topological materials
• Heavy-fermion systems
• Weyl semimetal
• Dynamical mean field theory
• First-principles calculations
• Tight-binding model