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Quantum Hall States of High Symmetry

Chetan Nayak·Frank Wilczek
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Abstract

We identify some hidden symmetries of Chern-Simons theories, such as appear in the effective theory for quantized Hall states. This allows us to determine which filling fractions admit spin-singlet quantum Hall states. Our results shed some light on states already observed at $ν=2/3$, and transitions between them. We identify SU(2), or higher, symmetries of many additional states -- including spin-polarized states. Our symmetries classify low-lying excited states and may be of use in the construction of trial wavefunctions, but are typically not present in the edge theory, where they are lifted by non-universal couplings.

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Chetan Nayak, Frank Wilczek. 1995-01-19. Quantum Hall States of High Symmetry. https://doi.org/10.1016/0550-3213(95)00271-s

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