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 moiré bands of magic angle twisted bilayer graphene (MATBG). For moiré band filling $3>|\nu |>2$, where superconductivity is strongest, we obtain evidence that the ground state is a spin ferromagnet. Near $|\nu |=3$, 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.

7 pages, 3 figures + SM: 7 pages, 14 figures