Acta Physica Polonica A

Mathematical Structure of Bosonic and Fermionic Jack States and Their Application in Fractional Quantum Hall Effect

Bartosz Kuśmierz, Ying-Hai Wu, Arkadiusz Wójs

Published Nov 1, 2014• 6 citations

Abstract

Fractional quantum Hall eect is a remarkable behaviour of correlated electrons, observed exclusively in two dimensions, at low temperatures, and in strong magnetic elds.The most prominent fractional quantum Hall state occurs at Landau level lling factor ν = 1/3 and it is described by the famous Laughlin wave function, which (apart from the trivial Gaussian factor) is an example of Jack polynomial.Fermionic Jack polynomials also describe another pair of candidate fractional quantum Hall states: MooreRead and ReadRezayi states, believed to form at the ν = 1/2 and 3/5 llings of the second Landau level, respectively.Bosonic Jacks on the other hand are candidates for certain correlated states of cold atoms.We examine here a continuous family of fermionic Jack polynomials whose special case is the Laughlin state as approximate wave functions for the 1/3 fractional quantum Hall eect.

DOI: 10.12693/aphyspola.126.1134

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