Ground state of two-dimensional electrons and the reversed spins in the fractional quantum Hall effect

Abstract

We have diagonalized numerically the Hamiltonian of a two-dimensional electron system of finite size, allowing some electron spins to be antiparallel to the magnetic field, in the lowest Landau level. We find that, in the case of the filling fraction $\ensuremath{\nu}=\frac{p}{q}$, with $q$ odd and $pg1$, the ground state with nonpolarized spins is energetically favored. The present results also indicate that filling factors $\ensuremath{\nu}=\frac{4}{9}$ and $\ensuremath{\nu}=\frac{4}{11}$ might be observable experimentally with partially polarized electron spins. At $\ensuremath{\nu}=\frac{1}{3}$ the spatial wave function for the ground state is found to be totally antisymmetric.