We demonstrate that a finite-doping quantum critical point (QCP) naturally descends from the existence of a first-order Mott transition in the phase diagram of a strongly correlated material. In a prototypical case of a first-order Mott transition the surface associated with the equation of state for the homogeneous system is ”folded” so that in a range of parameters stable metallic and insulating phases exist and are connected by an unstable metallic branch.
We show that tuning the chemical potential causes the zero-temperature equation of state to gradually unfold. Under general conditions, we find that the Mott transition evolves into a first-order transition between two metals, associated to a phase separation region ending in the finite-doping QCP. This scenario is demonstrated by solving a simple multi-orbital Hubbard model relevant for the Iron-based superconductors, but its origin - the splitting of the atomic ground state multiplet by a small energy scale, here Hund’s coupling - is much more general. A strong analogy with cuprate superconductors is traced.
 Chatzieleftheriou et al., Phys. Rev. Lett. 130, 066401 (2023).