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We work with a Hubbard-like interaction that corresponds to the screened Coulomb interaction in a well-defined limit where the Thomas-Fermi screening length $l_\\text{TF}$ is much larger than monolayer graphene's lattice spacing $l_g \\ll l_\\text{TF}$ and much smaller than the Moir\\'e super lattice's spacing $ l_\\text{TF} \\ll l_{\\text{Moir\\'e}}$. 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