Competing Topological Orders in the ν=12/5 Quantum Hall State
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 t...
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ftunivmaynooth:oai:mural.maynoothuniversity.ie:10553 2023-05-15T16:55:48+02:00 Competing Topological Orders in the ν=12/5 Quantum Hall State Bonderson, Parsa Feiguin, Adrian E. Moller, Gunnar Slingerland, Joost 2012 text https://mural.maynoothuniversity.ie/10553/ https://mural.maynoothuniversity.ie/10553/1/JS-Competing-2012.pdf en eng American Physical Society https://mural.maynoothuniversity.ie/10553/1/JS-Competing-2012.pdf Bonderson, Parsa and Feiguin, Adrian E. and Moller, Gunnar and Slingerland, Joost (2012) Competing Topological Orders in the ν=12/5 Quantum Hall State. Physical Review Letters, 108 (036806). ISSN 1079-7114 Article PeerReviewed 2012 ftunivmaynooth 2022-06-13T18:46:25Z 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. Article in Journal/Newspaper IPY Maynooth University ePrints and eTheses Archive (National University of Ireland) |
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Open Polar |
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Maynooth University ePrints and eTheses Archive (National University of Ireland) |
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ftunivmaynooth |
language |
English |
description |
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. |
format |
Article in Journal/Newspaper |
author |
Bonderson, Parsa Feiguin, Adrian E. Moller, Gunnar Slingerland, Joost |
spellingShingle |
Bonderson, Parsa Feiguin, Adrian E. Moller, Gunnar Slingerland, Joost Competing Topological Orders in the ν=12/5 Quantum Hall State |
author_facet |
Bonderson, Parsa Feiguin, Adrian E. Moller, Gunnar Slingerland, Joost |
author_sort |
Bonderson, Parsa |
title |
Competing Topological Orders in the ν=12/5 Quantum Hall State |
title_short |
Competing Topological Orders in the ν=12/5 Quantum Hall State |
title_full |
Competing Topological Orders in the ν=12/5 Quantum Hall State |
title_fullStr |
Competing Topological Orders in the ν=12/5 Quantum Hall State |
title_full_unstemmed |
Competing Topological Orders in the ν=12/5 Quantum Hall State |
title_sort |
competing topological orders in the ν=12/5 quantum hall state |
publisher |
American Physical Society |
publishDate |
2012 |
url |
https://mural.maynoothuniversity.ie/10553/ https://mural.maynoothuniversity.ie/10553/1/JS-Competing-2012.pdf |
genre |
IPY |
genre_facet |
IPY |
op_relation |
https://mural.maynoothuniversity.ie/10553/1/JS-Competing-2012.pdf Bonderson, Parsa and Feiguin, Adrian E. and Moller, Gunnar and Slingerland, Joost (2012) Competing Topological Orders in the ν=12/5 Quantum Hall State. Physical Review Letters, 108 (036806). ISSN 1079-7114 |
_version_ |
1766046866379636736 |