Quantum phase transitions induced by the spin-orbit interaction in the N = 1 landau level

The effect of the spin-orbit interaction on the fractional quantum Hall states at filling factors ν = 7/3, 5/2, and 12/5 is studied by the exact diagonalization method and density-matrix renormalization group (DMRG) method. We calculate the excitation energy gap, ground-state pair-correlation functions, and the topological entanglement entropy to analyze the effect of the spin-orbit interaction. The obtained results show that, at ν = 7/3, the spin-orbit interaction destabilizes the parafermion state, leading to the phase transition to the Laughlin state. At ν = 5/2 the Pfaffian state is stabilized but the phase transition to the composite fermion liquid state finally occurs. At ν = 12/5, the parafermion ground state is destabilized and the phase transition to the Jain state occurs.