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We study the possibility of charge order at quarter filling andantiferromagnetism at half-filling in a tight-binding model of magic angletwisted bilayer graphene. We build on the model proposed by Kang and Vafek[Physical Review X 8(3), 031088 (2018)], relevant to a twist angle of$1.30^\circ$, and add on-site and extended density-density interactions.Applying the variational cluster approximation with an exact-diagonalizationimpurity solver, we find that the system is indeed a correlated (Mott)insulator at fillings $\frac14$, $\frac12$ and $\frac34$. At quarter filling,we check that the most probable charge orders do not arise, for all values ofthe interaction tested. At half-filling, antiferromagnetism only arises if thelocal repulsion $U$ is sufficiently large compared to the extendedinteractions, beyond what is expected from the simplest model of extendedinteractions.

Charge order and antiferromagnetism in twisted bilayer graphene from the variational cluster approximation