  We discuss the effect of long-range interactions within the self-consistent
Hartree-Fock (HF) approximation in comparison to short-range atomic Hubbard
interactions on the band structure of twisted bilayer graphene (TBG) at charge
neutrality for various twist angles. Starting from atomistic calculations, we
determine the quasi-particle band structure of TBG with Hubbard interactions
for various magnetic orderings: modulated anti-ferromagnetic (MAFM), nodal
anti-ferromagnetic (NAFM) and hexagonal anti-ferromagnetic (HAFM). Then, we
develop an approach to incorporate these magnetic orderings along with the HF
potential in the continuum approximation. Away from the magic angle, we observe
a drastic effect of the magnetic order on the band structure of TBG compared to
the influence of the HF potential. Near the magic angle, however, the HF
potential seems to play a major role on the band structure compared to the
magnetic order. These findings suggest that the spin-valley degenerate broken
symmetry state often found in HF calculations of charge neutral TBG near the
magic angle should favour magnetic order, since the atomistic Hubbard
interaction will break this symmetry in favour of spin polarization.
