intra-dimer magnetic interaction. These competing mechanisms are well known in strongly correlated systems tracing back to Doniach’s Kondo lattice [@doniach1977_kondo_lattice_weak_antiferromagnetism]. Not surprisingly, the R2B model is unable to provide a proper description of the system beyond the transition in the Mott insulator state (see Fig. \[fig:dimer\_transition\_spectra\]). We shall come back to this point later on.

We should mention here that, within the IPT approximation and our numerical precision, $\eta$ does not seem to vanish completely at intermediate values of $t_\perp$ ($\approx 0.5$) as clearly as it does for smaller and larger values (see Fig. \[fig:transition\_orderparam\]). We have also used CT-QMC at the lowest possible temperatures but the results were inconclusive due to the very small energy scale being in competition with the low temperature. This issue might be eventually fully resolved by better adapted methods such as NRG-DMFT [@bulla1998_numerical_renormalization_group_calculations_self] or DMRG-DMFT [@garcia2004_dynamical_mean_field_theory_with].

Insulator to metal transition across $U_{c_1}$ {#sec:orge8aebc9}
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An interesting feature of the solution of the DHM is the existence of a first order transition driven by temperature [@najera2017_resolving_vo2_controversy]. This transition emerges as a consequence of two coexistent solutions found in a region of the phase diagram of the model [@moeller1999_rkky_interactions_mott_transition] as we show in Fig. \[fig:DOS\_coex\].

![DOS 