An Exact Diagonalization Study of Twisted Bilayer Graphene at Integer Fillings: Charge Excitation*

Using exact diagonalization, we study the projected Hamiltonian with Coulomb interaction in the 8 flat bands of first magic angle twisted bilayer graphene. Employing the U(4)xU(4) symmetries in the chiral flat band limit, we reduce Hilbert space which allows for study near integer fillings. In the first chiral limit, we find that the ground states at these fillings are extremely well-described by Slater determinants in the Chern basis, and the exactly solvable charge excitations are the lowest charge excitations up to system sizes of 8x8 (for restricted Hilbert space). Physically, the excitations can be understood as adding electrons (holes) to empty bands (filled bands) with either the same or opposite chern number. Higher excitations constitute further U(4)xU(4) excitations on top of the additional particle and justify focusing on excitations close to the analytic and ED ground states. This agreement is apparent at smaller system sizes with the flat metric condition than without, justifying its validity.