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

TL;DR

This paper provides numerical evidence that daughter quantum Hall states can reliably identify the topological order of their parent non-Abelian phases, aiding in the classification of complex quantum states.

Contribution

It demonstrates that daughter states, identified through numerical methods, can predict the parent topological phase and distinguish between competing non-Abelian states.

Findings

Daughter states reliably predict parent topological phases.

Interactions stabilize specific non-Abelian states and their daughters.

Particle-hole symmetry-breaking influences Pfaffian versus anti-Pfaffian competition.

Abstract

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.