The numerical case for identifying paired quantum Hall phases by their daughters

Many candidate non-Abelian quantum Hall states are accompanied by nearby `daughter' states, which are proposed to identify their topological order. Combining exact diagonalization and trial wave functions, we provide numerical evidence that daughter states reliably predict the parent topological phase. In the contexts of bilayer graphene and wide GaAs quantum wells, we show that the same interactions simultaneously stabilize Pfaffian, anti-Pfaffian, and their daughters, while suppressing the Jain states. The competition between Pfaffian and anti-Pfaffian, which is decided by particle-hole symmetry-breaking interactions, can likewise be deduced from their daughters. These findings strongly support the daughter-state-based identification of non-Abelian quantum Hall phases.