Laughlin wave function and one-dimensional free fermions.

Abstract

Making use of the well-known phase-space reduction in the lowest Landau level, we show that the Laughlin wave function for the \ensuremath{\nu}=1/m case can be obtained exactly as a coherent-state representation of a 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.