The nature of the correlated states in twisted bilayer graphene (TBG) at the magic angle has received intense attention in recent years. We present a numerical study of an interacting Bistritzer-MacDonald (IBM) model of TBG using a suite of methods in quantum chemistry, including Hartree-Fock, coupled cluster singles, doubles (CCSD) and perturbative triples (CCSD(T)), as well as a quantum chemistry version of the density matrix renormalization group method (QC-DMRG). Our treatment of TBG is agnostic to gauge choices, and we present a new gauge-invariant formulation to detect the spontaneous symmetry breaking in interacting models. As part of our benchmarking, we explore the impact of different schemes for removing ``double-counting'' in the IBM model. Our results suggest that cross-validation of different IBM models, and perhaps ab initio interacting models may be needed for future studies of the TBG system.
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