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Topological entanglement Rényi entropy and reduced density matrix structure.
Steven T Flammia1, Alioscia Hamma, Taylor L Hughes
1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5 Canada.
Physical Review Letters
|April 7, 2010
Summary
Researchers generalized topological entanglement entropy to topological Rényi entropies. Surprisingly, these entropies are identical for all nonchiral topological phases, regardless of the parameter alpha.
Area of Science:
- Condensed matter physics
- Quantum information theory
Background:
- Topological entanglement entropy is a key tool for characterizing topologically ordered phases.
- Distinguishing between different topological phases often relies on finding robust topological invariants.
Purpose of the Study:
- To generalize topological entanglement entropy to a broader family of topological Rényi entropies.
- To investigate whether these generalized entropies can serve as new invariants for topological phases.
- To explore the structure of reduced density matrices in topologically ordered systems.
Main Methods:
- Generalization of topological entanglement entropy to a parametrized family of topological Rényi entropies.
- Analysis of the independence of these entropies from the parameter alpha for nonchiral topological phases.
Main Results:
- All topological Rényi entropies were found to be identical and independent of the parameter alpha for nonchiral topological phases.
- This unexpected result reveals a fundamental property of topologically ordered ground-state wave functions.
Conclusions:
- The independence of topological Rényi entropies from alpha indicates that no further universal information can be extracted from the entanglement spectrum for these phases.
- The generalized entropies do not provide new invariants beyond the standard topological entanglement entropy for nonchiral topological phases.
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