Controlled Phase Space Expansion for the Topological Heavy Fermion Model

We develop a controlled theoretical framework for topological heavy fermion (THF) models relevant to magic-angle twisted bilayer graphene (MATBG), where semimetallic conduction electrons hybridize with a lattice of interacting f-sites. By integrating out the localized electrons exactly, we derive an effective action for the conduction electrons with non-local in time, multi-fermion interactions dominated by flavor-flip processes. A small hybridization-phase-space parameter controls a systematic loop expansion, enabling nonperturbative calculations of quasiparticle properties and response functions. At leading order, the theory recovers the Hubbard I approximation, while higher-loop corrections yield frequency-dependent quasiparticle lifetimes and a Curie-Weiss scaling of the flavor susceptibility. This approach captures key correlation effects in MATBG across a wide range of dopings and interaction strengths, without relying on band projection or fixed-valence assumptions.