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

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

2009-01-30

arxiv.org/abs/0901.4965v4

Phys. Rev. Lett. 108, 036806 (2012)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 2 figures; v2: minor corrections; v3: new title, revised exposition, inclusion of neutral gap and finite well-width r

Scientific paper

10.1103/PhysRevLett.108.036806

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.

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