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Identifying non-Abelian topological order through minimal entangled states
W Zhu1, S S Gong1, F D M Haldane2
1Department of Physics and Astronomy, California State University, Northridge, California 91330, USA.
Physical Review Letters
|March 25, 2014
Summary
Researchers measured entanglement entropy to confirm non-Abelian topological order in topological band models. This study reveals Ising anyon and Fibonacci quasiparticle statistics in lattice models without prior wave function knowledge.
Area of Science:
- Condensed Matter Physics
- Quantum Information Science
Background:
- Topological order, characterized by long-range quantum entanglement, is not detectable by local measurements.
- Non-Abelian topological states are crucial for topological quantum computation.
Purpose of the Study:
- To establish non-Abelian topological order in topological band models using entanglement entropy.
- To investigate quasiparticle statistics of non-Abelian Moore-Read and Read-Rezayi states on lattice models.
Main Methods:
- Exact diagonalization of lattice models with bosonic particles.
- Measurement of entanglement entropy to identify minimal entangled states (MESs).
- Extraction of the modular S matrix from MESs.
Main Results:
- Identified multiple independent MESs in the ground state manifold on a torus.
- The extracted modular S matrix accurately reflects Ising anyon and Fibonacci quasiparticle statistics.
- Demonstrated quasiparticle quantum dimensions and fusion rules for these systems.
Conclusions:
- Unambiguously confirmed the topological nature of quantum states in flatband models.
- The method successfully characterizes topological order without relying on model wave functions.
- Provides a robust approach for identifying non-Abelian topological phases.
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