Competing Topological Orders in the nu=12/5 Quantum Hall State

Understand

We provide numerical evidence that a p_{x}-i p_{y} paired Bonderson--Slingerland (BS) non-Abelian hierarchy state is a strong candidate for the observed nu=12/5 quantum Hall plateau.

• We confirm the existence of a gapped incompressible nu = 12/5 quantum Hall state with shift S=2 on the sphere, matching that of the BS state.
• The exact ground state of the Coulomb interaction at S=2 is shown to have large overlap with the BS trial wave function.
• Larger overlaps are obtained with BS-type wave functions that are hierarchical descendants of general p_{x}-i p_{y} weakly-paired states at nu=5/2.