2005/09/30 by Emil J. Bergholtz, A. Karlhede, Anders Karlhede
Engineering · Materials Science · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Electron #Graphene research and applications #Physics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Theoretical physics #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1088/1742-5468/2006/04/l04001
published as J. Stat. Mech. (2006) L04001 · 4 pages, 1 figure
arxiv created 2005/11/21 · openalex publication_date 2006/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the lowest Landau level on a torus as a function of its circumference L 1 . When L 1 → 0, the ground state at general rational filling fraction is a crystal with a gap—a Tao–Thouless state. For filling fractions ν = p /(2 pm + 1), these states are the limits of Laughlin's or Jain's wavefunctions describing the gapped quantum Hall states when L 1 → ∞ . 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 L 1 ∼ 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 L 1 → ∞ . Furthermore, the effective Landau level structure that emerges within the lowest Landau level is found to be a consequence of the magnetic symmetries.