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We revisit the localized Wannier state description of the twisted bilayergraphene, focusing on the chiral limit. We provide a simple method forconstructing such 2D exponentially localized -- yet valley polarized -- Wannierstates, centered on the sites of the honeycomb lattice, paying particularattention to maintaining all the unobstructed symmetries. This includes theunitary particle-hole symmetry, and the combination of $C_2\mathcal{T}$ and thechiral particle-hole symmetry. The $C_2\mathcal{T}$ symmetry alone remainstopologically obstructed and is not represented in a simple site-to-sitefashion. We also analyze the gap and the dispersion of single particle andsingle hole excitations above a strong coupling ground state at integerfillings, which we find to be dominated by the on-site and the nearest neighborterms of a triangular lattice hopping model, with a minimum at the center ofthe moire Brillouin zone. Finally, we use the insight gained from this realspace description to understand the dependence of the gap and the effectivemass on the range of the screened Coulomb interaction.

Lattice model for the Coulomb interacting chiral limit of the magic angle twisted bilayer graphene: symmetries, obstructions and excitations