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Competing topological orders in the ν=12/5 quantum Hall state
Parsa Bonderson1, Adrian E Feiguin, Gunnar Möller
1Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA.
Physical Review Letters
|March 10, 2012
Summary
Numerical evidence suggests a p(x)-ip(y) paired Bonderson-Slingerland (BS) state explains the ν=12/5 quantum Hall plateau. This non-Abelian topological order shows a strong candidate match, confirmed by ground state analysis.
Area of Science:
- Condensed matter physics
- Quantum Hall effect
- Topological phases of matter
Background:
- The quantum Hall effect exhibits exotic states at fractional filling factors.
- Non-Abelian states are crucial for topological quantum computing.
- Identifying specific non-Abelian states experimentally is a key challenge.
Purpose of the Study:
- To identify the specific non-Abelian topological order responsible for the observed ν=12/5 quantum Hall plateau.
- To investigate the properties of the Bonderson-Slingerland (BS) state as a candidate.
- To compare the BS state with other competing non-Abelian states.
Main Methods:
- Numerical simulations to provide evidence for candidate states.
- Calculation of ground state properties and overlaps with trial wave functions.
- Finite-size scaling analysis of ground-state energies.
- Comparison of the ν=12/5 state with the BS (S=2) and Read-Rezayi (S=-2) universality classes.
Main Results:
- Numerical evidence strongly supports the p(x)-ip(y) paired Bonderson-Slingerland (BS) state as a candidate for the ν=12/5 quantum Hall plateau.
- A gapped incompressible ν=12/5 quantum Hall state with shift S=2 was confirmed, matching the BS state.
- The exact ground state of Coulomb interaction at S=2 shows large overlap with the BS trial wave function.
- Hierarchical descendants of p(x)-ip(y) weakly paired states at ν=5/2 yield even larger overlaps.
- Finite-size scaling reveals a tight competition between the BS (S=2) and 3-clustered Read-Rezayi (S=-2) non-Abelian topological orders.
Conclusions:
- The Bonderson-Slingerland non-Abelian hierarchy state is a compelling candidate for the observed ν=12/5 quantum Hall plateau.
- The study confirms the existence and properties of this state, highlighting its potential.
- Further research is needed to distinguish between the closely competing BS and Read-Rezayi topological orders at ν=12/5.
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