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

TL;DR

This paper provides numerical evidence that a specific non-Abelian quantum Hall state is a strong candidate for the nu=12/5 plateau, showing a close competition between two topological orders.

Contribution

It demonstrates the existence of a gapped non-Abelian quantum Hall state at nu=12/5 with detailed numerical analysis and comparison to competing topological orders.

Findings

Large overlap of Coulomb ground state with BS trial wave function

Finite size scaling shows competition between two non-Abelian orders

Matching shift S=2 confirms the state as a candidate for nu=12/5

Abstract

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. We perform a finite size scaling analysis of the ground state energies for nu=12/5 states at shifts corresponding to the BS (S=2) and 3-clustered Read-Rezayi (S=-2) universality classes. This analysis reveals very tight competition between these two non-Abelian topological orders.