  We investigate the metal-to-insulator phase transition driven by the
density-density electronic interaction in the quarter-filled model on a cubic
lattice with two orbitals split by a crystal field. We show that a systematic
consideration of the non-local collective electronic fluctuations strongly
affects the picture of the phase transition provided by the dynamical mean
field theory. Our calculations reveal the appearance of metallic and Mott
insulating states characterised by the same density but different values of the
chemical potential, which is missing in the local approximation to electronic
correlations. We find that the region of concomitant metastability of these two
solutions is remarkably broad in terms of the interaction strength. It starts
at a critical value of the interaction slightly larger than the bandwidth and
extends to more than twice the bandwidth, where the two solutions merge into a
Mott insulating phase. Our results illustrate that non-local correlations can
have crucial consequences on the electronic properties in the strongly
correlated regime of the simplest multi-orbital systems.
