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. Our theory focuses on an energy window where the interactions can be treated perturbatively within the THF model, providing insights into the low-energy physics. In particular, 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.