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

• Main Authors: Bonderson, Parsa, Feiguin, Adrian E., Moller, Gunnar, Slingerland, Joost
• Format: Article in Journal/Newspaper
• Language: English
• Published: American Physical Society 2012
• Subjects: IPY
• Online Access: https://mural.maynoothuniversity.ie/10553/; https://mural.maynoothuniversity.ie/10553/1/JS-Competing-2012.pdf

We provide numerical evidence that a px−ipy paired Bonderson-Slingerland (BS) non-Abelian hierarchy state is a strong candidate for the observed ν=12/5 quantum Hall plateau. We confirm the existence of a gapped incompressible ν=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 a large overlap with the BS trial wave function. Larger overlaps are obtained with BS-type wave functions that are hierarchical descendants of general px−ipy weakly paired states at ν=5/2. We perform a finite-size scaling analysis of the ground-state energies for ν=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.