Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene*

We present new theoretical results about correlated states observed in magic angle twisted bilayer graphene obtained using finite-size exact-diagonalization calculations. Starting from the continuum model of flat moir´e bands, we investigate interaction effects in effective model with allowed fluctuations of occupation numbers within two flat bands of magic angle twisted bilayer graphene and self-energies of fully occupied frozen remote valence bands in graphene's negative-energy sea. We consider filling factors above |2|, which includes a filling factor range, where superconductivity is strongest. Spin and valley polarization for both, integer and non-integer filling factors, is determined. A comparison of exact-diagonalization calculations with Hartree-Fock method results allows us to determine the role of correlation effects. We analyze the response of the system to an external field that couples to sublattice polarization. An intepretation of the systems as generalized ferromagnet with filling factor dependent anisotropy energy related to spin, valley, and sublattice polarization is discussed.