Odd-parity altermagnetism (ALM) extends compensated collinear magnetism beyond the even-parity spin splitting of conventional altermagnets, but its role in correlated topological phases remains largely unexplored. Using the cluster slave-spin method, we show that the odd-parity ALM appearing in the ALM Chern-insulating phase of the Haldane-Hubbard model significantly reconstructs the local distribution of the Berry curvature in the conventional Chern-insulating phase, while the total Chern number remains unchanged compared to the Chern-insulating phase. The Berry curvature becomes spin and valley selective, zigzag ribbons develop nonsymmetric chiral edge states, while armchair ribbons remain inversion symmetric. The optical response mirrors this separation between the local reconstruction and the global topology: low-energy spectra are governed by quasiparticles near the gap, whereas the low-frequency Hall conductivity stays quantized, ${\sigma }_{\mathrm{T}\uparrow }(\mathrm{\Omega }\to 0)={\sigma }_{\mathrm{T}\downarrow }(\mathrm{\Omega }\to 0)=e^2/h$. These results establish the Haldane-Hubbard model as a minimal correlated platform for odd-parity altermagnetic topology.

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• Electronic structure
• Magnetic anisotropy
• Magnetism
• Topological edge modes
• Topological phases of matter
• Altermagnets
• Magnetic systems
• Strongly correlated systems
• Two-dimensional electron system
• Approximation methods for many-body systems
• Electron-correlation calculations
• Mean field theory
• Non-Fermi-liquid theory