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Non-Abelian anyons: when Ising meets Fibonacci.
1Department of Physics, University of Illinois, 1110 West Green Street, Urbana Illinois 61801-3080, USA.
Physical Review Letters
|October 2, 2009
Summary
This study explores interfaces between non-Abelian quantum Hall states, revealing neutral excitations described by conformal field theory. It examines quantum statistics mismatches between Ising and Fibonacci anyons.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Topological Quantum Computation
Background:
- Non-Abelian quantum Hall states exhibit exotic anyonic excitations.
- Interfaces between different topological phases can host novel physics.
- Moore-Read and k=2 non-Abelian spin-singlet states support Ising and Fibonacci anyons, respectively.
Purpose of the Study:
- To investigate the physics of an interface between the Moore-Read and k=2 non-Abelian spin-singlet quantum Hall states.
- To characterize the neutral excitations at this interface.
- To understand the implications of differing anyon statistics.
Main Methods:
- Analysis of the interface using conformal field theory (CFT).
- Characterization of excitations as described by a (1+1)-dimensional CFT.
- Examination of quasiholes and their quantum statistical properties.
Main Results:
- The interface supports neutral excitations governed by a CFT with central charge c=7/10.
- The CFT framework captures the behavior of excitations at the interface.
- The study highlights the impact of mismatched quantum statistics.
Conclusions:
- The interface between these two specific non-Abelian quantum Hall states is theoretically described by a c=7/10 CFT.
- This theoretical framework provides insights into the interplay of different anyonic systems.
- Understanding such interfaces is crucial for advancements in topological quantum computation.
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