Competing Topological Orders in the nu=12/5 Quantum Hall State
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.
Keywords
Cite
@article{arxiv.0901.4965,
title = {Competing Topological Orders in the nu=12/5 Quantum Hall State},
author = {Parsa Bonderson and Adrian E. Feiguin and Gunnar Moller and J. K. Slingerland},
journal= {arXiv preprint arXiv:0901.4965},
year = {2012}
}
Comments
5 pages, 2 figures; v2: minor corrections; v3: new title, revised exposition, inclusion of neutral gap and finite well-width results; v4: minor corrections