Recent angle-resolved photoemission spectroscopy (ARPES) and density functional theory plus Hubbard $U$ ($\mathrm{DFT}+U$) studies revealed that a heavy-fermion superconductor ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ exhibits Van Hove singularities and the Dirac point near the Fermi level $E_{\mathrm{F}}$, which are key signatures of strong-correlation effects and quantum geometry. We have constructed a two-dimensional 12-orbital Dirac-Anderson model as an effective model for ${\mathrm{CeRh}}_2{\mathrm{As}}_2$. The band structure and Fermi-surface topology of the Dirac-Anderson model agree well with the ARPES data and the $\mathrm{DFT}+U$ calculations. We show that the quantum geometry strongly favors magnetic-monopole fluctuations because of the Dirac point at the $M$ point. By solving the linearized Éliashberg equation, we demonstrate that the $B_{1u}$ and $B_{2g}$ representations, spin-triplet states originating from the Dirac point, exhibit the leading superconducting instabilities. By comparing the random-phase approximation and the fluctuation-exchange approximation, we further demonstrate that strong-correlation effects mitigate the influence of quantum geometry. The phase diagram of ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ under pressure is discussed in connection with the theoretical results.

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• Multipole order
• Spin fluctuations
• Superconductivity
• Heavy-fermion systems