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Effective 1d Language For Fractional Quantum Hall States, John Flavin

Arts & Sciences Electronic Theses and Dissertations

In the theory of the fractional quantum Hall effect, much attention is paid to the correspondence between fractional quantum Hall wave functions and conformal blocks in certain rational conformal field theories (CFT). This correspondence is powerful, enabling the calculation of the fractional statistics of a state that would be difficult if not impossible to calculate directly from the wave functions. But it is, in general, conjectural, remaining without microscopic justification in many cases of interest, and involves heavy mathematical machinery. We detail an alternative method to calculate Abelian and non-Abelian fractional statistics, the coherent state method. The method relies on …