  Although the strongly interacting flat bands in twisted bilayer graphene
(TBG) have been approached using the minimal Bistritzer-MacDonald (BM)
Hamiltonian, there is mounting evidence that strain and lattice relaxation are
essential in correctly determining the order of the correlated insulator
groundstates. These effects can be incorporated in an enhanced continuum model
by introducing additional terms computed from the relaxation profile. To
develop an analytical and physical understanding of these effects, we include
strain and relaxation in the topological heavy fermion (HF) model of TBG. We
find that strain and relaxation are very well captured in first order
perturbation theory by projection onto the fully symmetric HF Hilbert space,
and remarkably do not alter the interacting terms in the periodic Anderson
model. Their effects are fully incorporated in the single-particle HF
Hamiltonian, and can be reproduced in a minimal model with only 4
symmetry-breaking terms. Our results demonstrate that the heavy fermion
framework of TBG is an efficient and robust representation of the perturbations
encountered in experiment.
