Kukushkin et al. have measured the electron spin polarization versus magnetic field in the fractional quantum Hall states. The polarization curves show wide plateaus and small shoulders. The 2D electron system is described by the total Hamiltonian ( ). Therein, is the sum of the Landau energies and classical Coulomb energies. is the residual interaction yielding Coulomb transitions. It is proven for any filling factor that the most uniform electron configuration in the Landau states is only one. The configuration has the minimum energy of . When the magnetic field is weak, some electrons have up-spins and the others down-spins. Then, there are many spin arrangements. These spin arrangements give the degenerate ground states of . We consider the partial Hamiltonian only between the ground states. The partial Hamiltonian yields the Peierls instability and is diagonalized exactly. The sum of the classical Coulomb and spin exchange energies has minimum for an interval modulation between Landau orbitals. Using the solution with the minimum energy, the spin polarization is calculated which reproduces the wide plateaus and small shoulders. The theoretical result is in good agreement with the experimental data. 1. Introduction In this paper, we examine the electron spin polarization in the FQH states with the filling factor . Before the examination, we see here the investigations on the FQHE briefly. The fractional quantum Hall effect was discovered by Pan et al. [1, 2]. The quasi particle with a fractional charge and its wave function were introduced by Laughlin using the variational method [3, 4]. Many physicists developed it [5–7]. Jain proposed the composite fermion theory [8, 9]. Thereafter, the FQH states with the nonstandard filling factors have been investigated by employing various methods as in the references [10–14]. These theories assume the various types of the quasi particles and their mixing. On the other hand, Tao and Thouless [15, 16] examined the case that the lowest Landau levels are partially filled with electrons. Their method is very important to investigate the FQH states. We have developed the Tao-Thouless theory and have found the most uniform configuration of electrons. It has been proven that the configuration is unique for any filling factor [17]. The configuration minimizes the expectation value of the total Hamiltonian. The Coulomb transitions conserve the component of the total momentum where the -direction indicates the current direction. The conservation law produces energy gaps for the specific filling factors. For the other
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