Quantum Phase Transitions Induced by the Spin--Orbit Interaction in the N = 1 Landau Level

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The effect of the spin--orbit interaction on the fractional quantum Hall states at filling factors \nu = 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 \nu=7/3, the spin--orbit interaction destabilizes the parafermion state, leading to the phase transition to the Laughlin state. At \nu=5/2 the Pfaffian state is stabilized but the phase transition to the composite fermion liquid state finally occurs. At \nu=12/5, the parafermion ground state is destabilized and the phase transition to the Jain state occurs.
2012-03-15