divergent mass is a hallmark of the metal-insulator transition in the single band Hubbard model within DMFT [@georges1996_dynamical_mean_field_theory_strongly]. That transition is a realization of the well-known Brinkman-Rice scenario, where the effective mass diverges at the metal-insulator transition. In the present dimer model we shall see that, despite a large renormalization of the effective mass, it does not diverge and the transition is qualitatively different.

![Low frequency scaling of the metallic DOS from Fig.\[fig:dimer\_transition\_spectra\] for increasing $U$ at fixed $t_\perp =0.3$. Right panels show a zoom into the corresponding low frequency region that is indicated with green lines in the left panels. The local spectral function (black lines) is decomposed in the Bonding Spectral function (Blue line) and Anti-bonding Spectral function(orange dot dashed line). The dashed red line is the renormalized parametrization of the low energy quasiparticle from equation . The superposition of the two bands decreases as the system approaches the critical value $U_{c_2}\approx 3.47$. The size of the superposition is the vanishing scale $\eta$, which in this scaled plot is $\eta/ZD = 1 - \tilde{t}_\perp/D$. \[fig:transition\_spectra\_scaling\]](dimer_transition_spectra_scaling.pdf){width="\linewidth"}

Motivated by the previous discussion and by Eqs.\[eq:tpeff\] and \[eq:low\_energy\_dos\] of the renormalized two band model, we close-up on the low frequency peak 