One-Dimensional Theory of the Quantum Hall System

Details One-Dimensional Theory of the Quantum Hall System One-Dimensional Theory of the Quantum Hall System

2005-09-16

arxiv.org/abs/cond-mat/0509434v2

J. Stat. Mech. (2006) L04001

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 1 figure

Scientific paper

10.1088/1742-5468/2006/04/L04001

We consider the lowest Landau level on a torus as a function of its circumference $L_1$. When $L_1\to 0$, the ground state at general rational filling fraction is a crystal with a gap--a Tao-Thouless state. For filling fractions $\nu=p/(2pm+1)$, these states are the limits of Laughlin's or Jain's wave functions describing the gapped quantum Hall states when $L_1\to \infty$. For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral dipoles, or rather to a Luttinger liquid modification thereof, at $L_1\sim5$ magnetic lengths. This state is a version of the Rezayi-Read state, and develops continuously into the state that is believed to describe the observed metallic phase as $L_1\to \infty$. Furthermore, the effective Landau level structure that emerges within the lowest Landau level follows from the magnetic symmetries.

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