Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies

We study the two-dimensional electron gas in a high magnetic field at filling factor =1 for an arbitrary ratio of the Zeeman energy g₁B to the typical interaction energy. We find that the system always has a gap, even when the one-particle gap vanishes, i. e. , when g=0. When g is sufficiently large, the quasiparticles are perturbatively related to those in the noninteracting limit; we compute their energies to second order in the Coulomb interaction. For g smaller than a critical value g₂ the quasiparticles change character; in the limit of g0, they are skyrmions---spatially unbounded objects with infinite spin. In GaAs heterojunctions, the gap is unambiguously predominantly due to correlation effects; indeed, we tentatively conclude that g is always smaller than g₂, so the relevant quasiparticles are the skyrmions. The generalization to other odd-integer filling factors, and to =1/3 and 1/5, is discussed.