The extension of single-site coherent potential approximation (CPA) to multiorbital Hubbard models with full Hund's coupling has remained challenging due to the difficulty of constructing an appropriate alloy-analogy model. Here, we decompose the exact Green's functions of the atomic-limit two-orbital Hubbard model with full Hund's coupling into pole expansions, enabling the construction of the alloy-analogy model and thus facilitating the development of an extended two-orbital CPA that incorporates spin-flip and pair-hopping terms beyond previous treatments. Applying this method to the two-orbital Hubbard model on square lattice, we reveal a metallic phase stabilized around $U^{\prime }=U/2$, which is absent in earlier studies, and identify a rapid growth in the on-site interorbital doublon-holon correlation for $U^{\prime }>U/2$. This phase and the evolution of the doublon-holon state are elucidated through the exact atomic-limit Green's function solution. The effect of distinct Hund's coupling components is also examined.

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• Phase diagrams
• Quantum phase transitions
• Quasiparticles & collective excitations
• Strongly correlated systems
• Coherent potential approximation
• Green's function methods
• Hubbard model