Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene
Abstract
We report on finite-size exact-diagonalization calculations in a Hilbert space defined by the continuum-model flat moir\'e bands of magic angle twisted bilayer graphene (MATBG). For moir\'e band filling 3>||>2, where superconductivity is strongest, we obtain evidence that the ground state is a spin ferromagnet. Near ||=3, we find Chern insulator ground states that have spontaneous spin, valley, and sublattice polarization, and demonstrate that the anisotropy energy in this order-parameter space is strongly band-filling-factor dependent. We emphasize that inclusion of the remote band self-energy is necessary for a reliable description of MATBG flat band correlations.
0