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The anisotropic two‐orbital Hubbard model with different bandwidths and degrees of frustration in each orbital is investigated in the framework of both single‐site dynamical mean‐field theory (DMFT) as well as its cluster extension (DCA) for clusters up to four sites combined with a continuous‐time quantum Monte Carlo algorithm. This model shows a rich phase diagram which includes the appearance of orbital selective phase transitions, non‐Fermi liquid behavior as well as antiferromagnetic metallic states. We discuss the advantages and drawbacks of employing the single‐site DMFT with respect to DCA and the consequences for the physical picture obtained out of these calculations. Finally, we argue that such a minimal model may be of relevance to understand the nature of the antiferromagnetic metallic state in the iron‐pnictide superconductors as well as the origin of the small staggered magnetization observed in these systems.

Anisotropic two‐orbital Hubbard model: Single‐site versus cluster Dynamical Mean‐Field Theory