Finite Temperature Magnetism in Fractional Quantum Hall Systems: Composite Fermion Hartree-Fock and Beyond

Abstract

Using the Hamiltonian formulation of Composite Fermions developed recently, the temperature dependence of the spin polarization is computed for the translationally invariant fractional quantum Hall states at $ν=1/3$ and $ν=2/5$ in two steps. In the first step, the effect of particle-hole excitations on the spin polarization is computed in a Composite Fermion Hartree-Fock approximation. The computed magnetization for $ν=1/3$ lies above the experimental results for intermediate temperatures indicating the importance of long wavelength spin fluctuations which are not correctly treated in Hartree-Fock. In the second step, spin fluctuations beyond Hartree-Fock are included for $ν=1/3$ by mapping the problem on to the coarse-grained continuum quantum ferromagnet. The parameters of the effective continuum quantum ferromagnet description are extracted from the preceding Hartree-Fock analysis. After the inclusion of spin fluctuations in a large-N approach, the results for the finite-temperature spin polarization are in quite good agreement with the experiments.