Strong interactions in twisted bilayer graphene at the magic angle

Twisted bilayer graphene (TBG) has been an active area of research due to its promise as a novel material with remarkable tunable properties. We perform a fully self-consistent Hartree-Fock calculation on the lattice accounting for the Coulomb interaction among all the sites(more than 10,000) of the moiré unit cell at the magic angle. We derive the fully self-consistently reconstructed bands at the Hartree-Fock level as a function of the filling factor. Considering rotations around AA sites, which permit constructing exponentially localized Wannier orbitals without topological obstructions, we derive an effective lattice model for the mini-bands of TBG accounting for spin and valley quantum numbers. We numerically address their possible many-body insulating phases at various filling factors.