  We investigate correlated insulating states in magic-angle twisted bilayer
graphene (TBG) by the exact diagonalization method applied to the extended
Hubbard model with interaction parameters recently evaluated in the realistic
effective model. Our model can handle the competing interactions among Wannier
orbitals owing to their significant overlap, which is a crucial but overlooked
aspect of the magic-angle TBG. We propose two candidates for the correlated
insulating states: spin- and valley-ferromagnetic band insulator and the Dirac
semimetallic state for two flavors with peculiar renormalization, where a
flavor denotes a combined degree of freedom with spin and valley. One of the
important consequences for the latter candidate is that it allows van Hove
singularity near half-filling of the whole band structure (i.e. near the Dirac
points) to play some role in superconductivity. The consistency between the two
flavor degrees of freedom for the Dirac semimetallic state and the two-fold
degeneracy of the Landau level observed in the experiment is also noteworthy.
