Emil J Bergholtz and Anders Karlhede J. Stat. Mech. (2006) L04001 doi:10.1088/1742-5468/2006/04/L04001
Emil J Bergholtz and Anders Karlhede
Show affiliationsWe 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.
E-print Number: cond-mat/0509434
Cited: by |
Refers: to
73.43.Nq Quantum phase transitions
71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)
82D25 Crystals (For crystallographic group theory, see 20H15)
Issue 04 (April 2006)
Received 8 February 2006, accepted for publication 30 March 2006
Published 12 April 2006
Emil J Bergholtz and Anders Karlhede J. Stat. Mech. (2006) L04001
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