Electron-Electron Interactions in Twisted Bilayer Graphene

Abstract

In this paper we use exact diagonalization studies to explore the phase diagram of twisted bilayer graphene at the first magic angle. We show the physics in the flat band limit is closely related to the physics at a realistic bandwidth, inducing spin and valley polarization. We also show that the physics at realistic parameters can be described as a perturbation on the chiral limit with a large $U(4) \times U(4)$ symmetry which simplifies calculation greatly. This result may be used in the future to more easily calculate the many-body response as a function of single-body properties even when the interaction between electrons is strong.