Correlated insulator states in twisted bilayer graphene: Hartree-Fock studies

We discuss the correlated insulator states in twisted bilayer graphene (TBG) using two different types of Hartree-Fock (methods: in the first method all energy bands are included in the self-consistent calculations ,but some approximation is made for the Fock operators; in the other method, we project Coulomb interactions onto flat bands, and performed unrestricted Hartree-Fock calculations in the subspace of the flat bands. We have constructed the phase diagrams at even integer fillings of the flat bands in magic TBG, and discuss the experimental observables associated with different correlated insulator states.