The quantum Hall effects by now are recognized as prime examples of the importance of topological considerations in condensed-matter physics. The fractional Quantum Hall effect in particular has proven to display a large number of topologically ordered states that have been classified and understood in terms of hierarchical schemes. This review explains the current understanding of such classifications, with particular emphasis on conformal-field-theory approaches.
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Hansson et al. (2017) studied this question.
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