  We investigate the magnetic and metal-insulator (M-I) phase diagram of the
1/5-depleted square-lattice Hubbard model at 1/4 filling by the mean-field
approximation. There exist three magnetic phases of nonmagnetic (N),
antiferromagnetic (AF), and ferromagnetic (F) types, each realized for the
large intrasquare hopping t1, intersquare hopping t2, and Coulomb interaction
U, respectively. Within each magnetic phase, the M-I transition of Lifshitz
type emerges and, finally, six kind of phases are identified in the U-t1/t2
plane. When t1=t2, we find that the Dirac cone and nearly flat band around the
Gamma point form the SU(3) multiplet. The SU(3) effective theory well describes
the phase transitions between NI, paramagnetic-metal (PM), and AF phases. The
NI and AFI phases are characterized by different Berry phases as in
polyacetylene or graphene.
