Quantum Hall States of High Symmetry

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 $\nu =2/3$, 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.

17 pages, PostScript, 1 figure included. Revision - corrected slight error in equation (3.5) on Page 9

References in corpus (1)

• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$

Cited by in corpus (6)

• Modular Invariant Partition Functions in the Quantum Hall Effect
• Topological Phase Transition in the $\nu =2/3$ Quantum Hall Effect
• The breaking of quantum double symmetries by defect condensation
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Modular Invariants in the Fractional Quantum Hall Effect
• Invariant structure of the hierarchy theory of fractional quantum Hall states with spin