Controlled Loop Expansion for the Topological Heavy Fermion Model

We develop a controlled theoretical framework for the topological heavy fermion model relevant to magic-angle twisted bilayer graphene, where low density conduction electrons hybridize with a lattice of strongly interacting f-sites. By tracing out the localized electrons, we derive an effective action for the conduction electrons with long-range in time effective interactions, built from correlators of the single f-site problem. We identify a small hybridization-phase-space parameter resulting in a controlled loop expansion, enabling the derivation of nonperturbative results in either the interaction or the hybridization strength. To tree-level, the results are equivalent to the Hubbard I approximation. At higher loop order, we derive two key results applicable to temperatures above the flavor ordering temperature and below the on-site charging energy: 1) the quasi-particle lifetime, 2) the flavor susceptibility of the system. Remarkably, despite being strongly interacting, we find the susceptibility to accurately obey a Curie-Weiss law parametrically close to the Curie temperature.