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Braiding with Borromean Rings in (3+1)-Dimensional Spacetime
AtMa P O Chan1, Peng Ye1,2, Shinsei Ryu3
1Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Illinois 61801, USA.
Physical Review Letters
|August 25, 2018
Summary
Researchers discovered a new quantum phenomenon called Borromean rings braiding, distinct from the Aharonov-Bohm phase. This exotic braiding involves a particle and two loops, generating a unique phase related to topological quantum field theory.
Area of Science:
- Quantum Mechanics
- Topology
- Condensed Matter Physics
Background:
- The Aharonov-Bohm phase arises from particle winding around a loop.
- Existing topological phases are often linked to mutual winding between excitations.
Purpose of the Study:
- To explore novel braiding statistics beyond the Aharonov-Bohm effect.
- To introduce and analyze the Borromean rings braiding phenomenon.
Main Methods:
- Theoretical derivation of a new braiding phase.
- Utilizing concepts from knot theory, specifically Brunnian links.
- Formulating topological quantum field theories with AAB-type topological terms.
Main Results:
- A novel braiding phase, distinct from the Aharonov-Bohm phase, is identified.
- This phase arises from a particle interacting with two unlinked loops forming Borromean rings or Brunnian links.
- An explicit formula for the braiding phase is derived using Milnor's triple linking number.
Conclusions:
- The Borromean rings braiding represents a fundamentally new type of quantum phase.
- This discovery expands the understanding of topological phases in quantum systems.
- The proposed topological quantum field theories provide a framework for realizing these exotic braiding statistics.
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