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Non-abelian Quantum Hall States on the

Thin Torus

Published Jan 1, 2009• 0 citations
OpenAlex

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We propose a scheme to construct the most prominent Abelian and non-Abelian fractional quantum Hall states from K-component Halperin wave functions. In order to account for a one-component quantum Hall system, these SU(K) colors are distributed over all particles by an appropriate symmetrization. Numerical calculations corroborate the picture that K-component Halperin wave functions may be a common basis for both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.
To detect non-Abelian statistics in the $\ensuremath{\nu}=12∕5$ quantum Hall state through interferometry, we apply an analysis similar to the ones proposed for the non-Abelian $\ensuremath{\nu}=5∕2$ quantum Hall state. The result is that the amplitude of the Aharonov-Bohm oscillation of this interference is dependent on the internal states of quasiholes, but, in contrast to the $\ensuremath{\nu}=5∕2$ quantum Hall state, independent of the number of quasiholes. However, if the quasiholes are in a superposition state, it is necessary for the interferometer to have certain additional features to obtain the coefficients.