Quantum Hall States of High Symmetry

TL;DR

This paper uncovers hidden symmetries in Chern-Simons theories related to quantum Hall states, helping classify filling fractions and spin states, and providing insights into observed phenomena and state transitions.

Contribution

It reveals new hidden symmetries in effective theories of quantum Hall states, aiding classification and understanding of their properties.

Findings

Identifies symmetries in quantum Hall states at various filling fractions.

Explains the role of symmetries in classifying low-lying excitations.

Provides insights into observed states at ν=2/3 and their transitions.

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.