One-Dimensional Theory of the Quantum Hall System
2006 (Swedish)In: Bulletin of the American Physical Society, 2006Conference paper (Other academic)
We consider the lowest Landau level on a torus as a function of its circumference L1. When L1 → 0, the ground state at general rational filling fraction is a crystal with a gap—a Tao–Thouless state. For filling fractions ν = p/(2pm + 1), these states are the limits of Laughlin's or Jain's wavefunctions describing the gapped quantum Hall states when L1 → ∞. For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral fermions (dipoles), or rather to a Luttinger liquid modification thereof, at L1 ~ 5 magnetic lengths. Using exact diagonalization we identify this state as a version of the Rezayi–Read state, and find that it develops continuously into the state that is believed to describe the observed metallic phase as L1 → ∞. Furthermore, the effective Landau level structure that emerges within the lowest Landau level is found to be a consequence of the magnetic symmetries.
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IdentifiersURN: urn:nbn:se:su:diva-16750OAI: oai:DiVA.org:su-16750DiVA: diva2:183270