  Quantum materials featuring both itinerant and localized degrees of freedom
exhibit numerous exotic phases and transitions that deviate from the
Ginzburg-Landau paradigm. This work uses the composite operator formalism to
examine two-orbital strongly correlated Hubbard models. We observe the
spontaneous breaking of orbital symmetry, where the electron density in one of
the orbitals reaches half-filling, resulting in an orbitally selective Mott
phase (OSMP). This broken symmetry phase becomes unstable at a critical average
electronic density away from half-filling. Furthermore, significant orbital
differentiation persists up to a moderate inter-orbital hopping, beyond which
the system abruptly transitions to an orbitally uniform phase. In the OSMP
phase, the electrons in the two orbitals are weakly hybridized, resulting in a
small Fermi surface. The volume of the Fermi surface jumps at the transition
from the OSMP to the orbitally uniform phase. We also discuss the physical
mechanisms leading to the collapse of the OSMP phase under different
perturbations.
