Quantum Phase Transitions in Fractional Quantum Hall Effect of Graphene: Many-body Chern Number and Chirality Ferromagnetism*

Fractional quantum Hall (FQH) states of graphene with nearest neighbor (NN) and next nearest neighbor (NNN) interaction are investigated by the pseudopotential projected into the n = 0 Landau band on honeycomb lat- tice. Effects of lattice are fully included and the many-body Chern number for the degenerate multiplet defined by twisting the boundary condition is evaluated numerically.
Quantum phase transitions induced by modifying the interaction range are observed for the filling factor ν = 1/3 and 2/3 associated with the chirality ferromagnetism. We also calculate the many-body Chern number matrix specified by the diagonal/off diagonal twisted boundary conditions in chiral basis. We further discuss the results in relation to the conventional bilayer FQH states.