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

TL;DR

This paper explores the connection between abelian and non-abelian quantum Hall liquids and charge density waves, revealing that quantum number fractionalization in one and two dimensions are fundamentally equivalent.

Contribution

It extends previous results to non-abelian bosonic Hall states, establishing the equivalence of fractionalization paradigms across dimensions.

Findings

Abelian quantum Hall liquids are connected to charge density waves on a torus.

Non-abelian bosonic Hall states exhibit similar adiabatic connections.

Quantum number fractionalization in 1D and 2D are shown to be equivalent.

Abstract

Previously we have demonstrated that, on a torus, the abelian quantum hall liquid is adiabatically connected to a charge density wave as the smaller dimension of the torus is varied. In this work we extend this result to the non-abelian bosonic Hall state. The outcome of these works is the realization that the paradigms of quantum number fractionalization in one dimension (polyacetylene) and two dimensions (fractional quantum Hall effect) are in fact equivalent.