DMRG study of strongly interacting Z2 flatbands: a toy model inspired by twisted bilayer graphene

Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern=±1), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL's with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL's with the same magnetic field. In the first scenario -- which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene -- the opposite Chern LLL's are Kramer pairs, and thus there exists time-reversal symmetry (Z2). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry -- a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern |++...+> or all negative |--...+>. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.