  We propose an exactly solvable lattice model, motivated by the significance
of the extended Hubbard model ($t-U-V$ model) and inspired by the work of
Hatsugai and Kohmoto. The ground state exhibits a diverse array of phases,
including the charge-$4e$ condensed phase, the charge-$2e$ superconducting
phase, the half-filled insulating phase, the quarter-filled insulating phase,
the metallic phase, and an unconventional metallic phase. Among them, the
unconventional metallic phase could be of particular significance, for the
coexistence of electrons and pairs at zero energy. These findings are poised to
advance our understanding and exploration of strongly correlated physics.
