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Magnetic Tweezers for the Measurement of Twist and Torque
Published on: May 19, 2014
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Topological entanglement entropy with a twist.
Benjamin J Brown1, Stephen D Bartlett2, Andrew C Doherty2
1Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom.
Physical Review Letters
|December 17, 2013
Summary
Topological defects in the toric code model, known as twists, exhibit properties analogous to Ising anyons. Calculations confirm identical quantum dimensions and fusion rules between toric code defects and Ising anyons.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
- Topological Quantum Computation
Background:
- Topologically ordered models exhibit exotic properties, including anyonic excitations.
- Defects in these models, such as dislocations, can mirror the behavior of anyons.
- The toric code model is a prominent example of a topologically ordered system.
Purpose of the Study:
- To investigate the relationship between defects and excitations in the toric code model.
- To strengthen the analogy between toric code defects (twists) and Ising anyons.
- To utilize topological entanglement entropy as a tool for characterizing defects and excitations.
Main Methods:
- Explicit mathematical calculations were performed.
- Topological entanglement entropy was employed as a diagnostic tool.
- Properties of defects and excitations in the toric code were analyzed.
Main Results:
- The toric code model with twists and dyon excitations was shown to possess the same quantum dimensions as an Ising anyon model.
- The total quantum dimension for both systems was found to be identical.
- The fusion rules for the toric code defects and Ising anyons were demonstrated to be the same.
Conclusions:
- The analogy between toric code defects and Ising anyons is robustly supported by quantitative analysis.
- Topological entanglement entropy effectively characterizes the properties of defects and excitations.
- This finding deepens our understanding of topological order and its emergent phenomena.
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