Spin instabilities and quantum phase transitions in integral and fractional quantum Hall states

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The inter-Landau-level spin excitations of quantum Hall states at filling factors nu=2 and 4/3 are investigated by exact numerical diagonalization for the situation in which the cyclotron (hbar*omegac) and Zeeman (EZ) splittings are comparable. The relevant quasiparticles and their interactions are studied, including stable spin wave and skyrmion bound states. For nu=2, a spin instability at a finite value of epsilon=hbar*omegac-EZ leads to an abrupt paramagnetic to ferromagnetic transition, in agreement with the mean-field approximation. However, for nu=4/3 a new and unexpected quantum phase transition is found which involves a gradual change from paramagnetic to ferromagnetic occupancy of the partially filled Landau level as epsilon is decreased.