The discovery of the multiple $H\text{−}T$ phase diagram of ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ offers a new route to designing topological superconductors. Although weak-coupling theories explain the experimental phase diagram qualitatively, a quantitative discrepancy between them has discouraged a conclusive interpretation. In this Letter, we thoroughly study the effect of the Coulomb interaction and the phase diagrams of locally noncentrosymmetric superconductors. We reveal an even-odd parity transition and the enhancement of the parity transition field in strongly correlated superconductors, and an issue of ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ is resolved.

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• Electron-mediated pairing
• Phase diagrams
• Superconductivity
• Heavy-fermion systems
• Strongly correlated systems
• Topological materials
• Diagrammatic methods
• Eliashberg theory
• Green's function methods
• Hubbard model