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We present a relativistic formulation of the quantum Hall effect on Haldanesphere. An explicit form of the pseudopotential is derived for the relativisticquantum Hall effect with/without mass term. We clarify particular features ofthe relativistic quantum Hall states with the use of the exact diagonalizationstudy of the pseudopotential Hamiltonian. Physical effects of the mass term tothe relativistic quantum Hall states are investigated in detail. The mass termacts as an interpolating parameter between the relativistic andnon-relativistic quantum Hall effects. It is pointed out that the mass termunevenly affects the many-body physics of the positive and negative Landaulevels as a manifestation of the "parity anomaly". In particular, we explicitlydemonstrate the instability of the Laughlin state of the positive firstrelativistic Landau level with the reduction of the charge gap.

Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"