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Sufficient symmetry conditions for Topological Quantum Order
Zohar Nussinov1, Gerardo Ortiz
1Department of Physics, Washington University, St. Louis, MO 63130, USA. zohar@wustl.edu
Summary
We establish conditions for Topological Quantum Order using Gauge-Like Symmetries. This framework unifies understanding and identifies new systems, advancing quantum computing research.
Area of Science:
- Condensed Matter Physics
- Quantum Information Science
Background:
- Topological Quantum Order (TQO) is crucial for robust quantum computation.
- Existing methods for identifying TQO have limitations.
Purpose of the Study:
- To establish sufficient conditions for TQO at zero and finite temperatures.
- To introduce a unifying framework based on Gauge-Like Symmetries.
- To identify new physical systems exhibiting TQO.
Main Methods:
- Analysis of low-dimensional Gauge-Like Symmetries.
- Investigation of emergent symmetries in low-energy sectors.
- Examination of Hamiltonians for specific material compounds and models.
Main Results:
- Gauge-Like Symmetries provide a unifying principle for TQO.
- New systems like orbital-dependent spin exchange and p+ip superconductors exhibit TQO.
- Standard measures like spectral gaps and entanglement entropy are insufficient to confirm TQO.
Conclusions:
- Gauge-Like Symmetries are key to understanding and engineering TQO.
- Thermal fluctuations can impact quantum computing schemes despite spectral gaps.
- This work enables the design of novel systems with TQO beyond standard topological field theories.
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