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Previously we have demonstrated that, on a torus, the abelian quantum hallliquid is adiabatically connected to a charge density wave as the smallerdimension of the torus is varied. In this work we extend this result to thenon-abelian bosonic Hall state. The outcome of these works is the realizationthat the paradigms of quantum number fractionalization in one dimension(polyacetylene) and two dimensions (fractional quantum Hall effect) are in factequivalent.Comment: 4 pages, 2 figures, published versio

Abelian and Non-Abelian Hall Liquids and Charge-Density Wave: Quantum Number Fractionalization in One and Two Dimensions