Interacting models for twisted bilayer graphene: Towards a quantum chemistry approach

In recent years, magic angle twisted bilayer graphene (MATBG) has received intense attention due to its experimentally observed superconducting properties. However, the nature of the correlated states in MATBG has not yet been fully understood. Thus far, most computational studies of MATBG have been performed on small systems using exact diagonalization or on moderate systems at the Hartree-Fock (HF) level of theory. The large ratio between the Coulomb interaction and the dispersion of the flat bands suggests that post-HF effects may become significant in certain parameter regimes. We propose a quantum chemistry approach to study the interacting Bistritzer-MacDonald (IBM) model of MATBG. Our implementation uses the PySCF software package which allows us to perform HF and post-HF calculations on the same footing for problem sizes that are intractable using exact diagonalization techniques. This allows us to explore the many-body properties of MATBG with a spinless, valleyless IBM model at integer as well as non-integer filling using coupled-cluster based methods, such as CCSD and CCSD(T), as well as the quantum chemistry density matrix renormalization group (QC-DMRG) method. We also present a gauge-invariant formulation to detect the spontaneous symmetry breaking in interacting models.