Perturbative renormalization group approach to magic-angle twisted bilayer graphene using topological heavy fermion model

Abstract: We develop a perturbative renormalization group (RG) theory for the topological heavy fermion (THF) model, describing magic-angle twisted bilayer graphene (MATBG) as an emergent Anderson lattice. The realistic parameters place MATBG near an intermediate regime where the Hubbard interaction $U$ and the hybridization energy $\gamma$ are comparable, motivating the need for RG analysis. Our approach analytically tracks the flow of single-particle parameters and Coulomb interactions within an energy window below $0.1$ eV, providing implications for distinguishing between Kondo-like ($U\gg \gamma$) and projected-limit/Mott-semimetal ($U\ll \gamma$) scenarios at low energies. We show that the RG flows generically lower the ratio $U/\gamma$ and drive MATBG toward the chiral limit, consistent with the previous numerical study based on the Bistritzer-MacDonald model. The framework presented here also applies to other moir\'e systems and stoichiometric materials that admit a THF description, including magic-angle twisted trilayer graphene, twisted checkerboard model, and Lieb lattice, among others, providing a foundation for developing low-energy effective theories relevant to a broad class of topological flat-band materials.