interpretation to the puzzling presence of a mid-infrared peak in the optical conductivity of metallic nano-size islands observed during the transition [@qazilbash2007_mott_transition_vo2_revealed_by] in terms of a novel correlated “monoclinic” metal [@najera2017_resolving_vo2_controversy]. Model Hamiltonians that capture the key ingredients are also attractive for experimentalist as they provide useful insights within a more intuitive yet non-trivial physical framework for strongly interacting systems.

In the present paper we continue with this strategy and make new inroads into the investigation of the nature of the insulator and metallic states realized in the Dimer Hubbard Model (DHM) within CDMFT. Specifically we address the issue on the physical characterization of the insulator state. A key feature of our approach is to observe that the quantum impurity problem of the DHM has the same form as the respective quantum impurity problem of the DFT+CDMFT method on realistic lattices. In fact, we shall see that our model solution does capture in a simpler context several features already seen in DFT+CDMFT studies [@tomczak2007_effective_band_structure_correlated_materials; @tomczak2008_effective_bandstructure_insulating_phase_versus], such as the presence of renormalized coherent bands in the insulator.

The model Hamiltonian approach enables the systematic investigation of the whole parameter space, which sheds light on the interplay of physical mechanisms. We shall 