Strongly interacting phases in twisted bilayer graphene at the magic angle

Twisted bilayer graphene near the magic angle is known to have a cascade of insulating phases at integer filling factors of the low-energy bands. In this Letter we address the nature of these phases through an unrestricted, large-scale Hartree-Fock calculation on the lattice that self-consistently accounts for all electronic bands. Using numerically unbiased methods, we show that Coulomb interactions produce ferromagnetic insulating states at integer fillings $\ensuremath{\nu}\ensuremath{\in}[\ensuremath{-}3,3]$ with maximal spin polarization ${M}_{\text{FM}}=4\ensuremath{-}|\ensuremath{\nu}|$. We find that the $\ensuremath{\nu}=0$ state is a pure ferromagnet, whereas all other insulating states are spin-valley polarized. At odd filling factors $|\ensuremath{\nu}|=1,3$ those states have a quantum anomalous Hall effect with Chern number $\mathcal{C}=1$. Except for the $\ensuremath{\nu}=0,\ensuremath{-}2$ states, all other integer fillings have insulating phases with additional sublattice symmetry breaking and antiferromagnetism in the remote bands. We map the metal-insulator transitions of these phases as a function of the effective dielectric constant. Our results establish the importance of large-scale lattice calculations to faithfully determine the ground states of twisted bilayer graphene at integer fillings.