'One-dimensional' theory of the quantum Hall system
2006 (English)In: Journal of Statistical Mechanics: Theory and Experiment, no L04001Article in journal (Refereed) Published
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/(2pm + 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.
Place, publisher, year, edition, pages
2006. no L04001
Condensed Matter Physics
IdentifiersURN: urn:nbn:se:su:diva-14067DOI: doi:10.1088/1742-5468/2006/04/L04001OAI: oai:DiVA.org:su-14067DiVA: diva2:180587