Verwey transition in magnetite at high pressure: A new quantum critical point at the onset of metallization

We provide a detailed physical discussion of the existence of a quantum critical point   (QCP) at the metallization threshold of an almost stoichiometric magnetite, with the critical pressure pc=8GPa. A presence of an additional crossover or a critical line separating metallic and semiconducting states is proposed. A connection of the critical behavior to that of a spinless-fermion model with coupling of fermions to the lattice distortion is outlined.