Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands

We identify states favored by Coulomb interactions projected onto the Wannier basis of the four narrow bands of the magic angle twisted bilayer graphene. At the filling of 2 electrons/holes per moire unit cell, such interactions favor an insulating SU(4) ferromagnet. The kinetic terms select the ground state in which the two valleys with opposite spins are equally mixed, with a vanishing magnetic moment per particle. We also find extended excited states, the gap to which decreases in the magnetic field. An insulating stripe ferromagnetic phase is favored at 1 electron/hole per unit cell.