Extended Data Fig. 3: Exact diagonalization.
From: Cascade of electronic transitions in magic-angle twisted bilayer graphene
a, Theoretical spectral weight for different values of the filling ν calculated by exact diagonalization of the two-flavour, two-band Hubbard model consisting of 4 sites, interband separation 2E0 = 16 meV, nearest-neighbour hopping t = 0.6 meV, and on-site Coulomb repulsion U = 23 meV. Dashed black lines highlight the cascade features, which are fewer in number than in the experimental data because the theoretical model has only 2 flavours (compared to fourfold degeneracy in MATBG). b, The calculated chemical potential μ as a function of ν shows jumps at integer fillings. The inset schematically depicts the 4 AA sites, with on-site repulsion U and hopping t. c, Calculated energy difference E between cascade features and the chemical potential jump at ν = 1 as a function of U.
