General Many-Body Perturbation Framework for Moiré Systems

Moiré superlattices host a rich variety of correlated topological states, including interaction-driven integer and fractional Chern insulators. A common approach to study interacting ground states at integer fillings is the Hartree-Fock mean-field method. However, this method neglects dynamical correlations, which often leads to an overestimation of spontaneous symmetry breaking and fails to provide quantitative descriptions of single-particle excitations. This work introduces a general many-body perturbation framework for moiré systems, combining all-band Hartree-Fock calculations with random phase approximation (RPA) correlation energies and GW quasiparticle corrections. We apply this framework to hexagonal boron nitride aligned rhombohedral pentalayer graphene and magic-angle twisted bilayer graphene. We show that incorporating RPA correlation energy and GW self-energy corrections yields phase diagrams and single-particle spectra that quantitatively align with experimental measurements. Our versatile framework provides a systematic beyond-mean-field approach applicable to generic moiré systems.