Laughlin Wave Function and One-Dimensional Free Fermions

Abstract

Making use of the well-known phase space reduction in the lowest Landau level(LLL), we show that the Laughlin wave function for the $\nu =\frac{1}{m}$ case can be obtained exactly as a coherent state representation of an one dimensional $(1D)$ wave function. The $1D$ system consists of $m$ copies of free fermions associated with each of the $N$ electrons, confined in a common harmonic well potential. Interestingly, the condition for this exact correspondence is found to incorporate Jain's parton picture. We argue that, this correspondence between the free fermions and quantum Hall effect is due to the mapping of the $1D$ system under consideration, to the Gaussian unitary ensemble in the random matrix theory.

7 pages, Latex , no figures

References in corpus (6)

• Infinite Symmetry in the Quantum Hall Effect
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• "Peireles Substitution" and Chern-Simons Quantum Mechanics
• Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
• Gauge Theory Formulation of the $c=1$ Matrix Model: Symmetries and Discrete States

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• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• A novel realization of the Calogero-Moser scattering states as coherent states
• The inverse-square interaction phase diagram: unitarity in the bosonic ground state