U(2) CSGL theories are built for FQHE hierarchies, reproducing all known filling fractions and uniquely fixing topological orders while revealing a particle-hole symmetry between sequences.
The trivial insulator can be viewed as the particle-hole conjugate of theν= 1 inte- ger quantum Hall state
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$\mathrm{U}(2)$ Chern-Simons-Ginzburg-Landau Theory of Fractional Quantum Hall Hierarchies
U(2) CSGL theories are built for FQHE hierarchies, reproducing all known filling fractions and uniquely fixing topological orders while revealing a particle-hole symmetry between sequences.