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Global Anomaly Detection in Two-Dimensional Symmetry-Protected Topological Phases
Nick Bultinck1, Robijn Vanhove1, Jutho Haegeman1
1Department of Physics and Astronomy, Ghent University, Krijgslaan 281 S9, B-9000 Ghent, Belgium.
Physical Review Letters
|May 15, 2018
Summary
Symmetry-protected topological phases exhibit edge anomalies. This study analyzes two-dimensional bosonic phases, connecting anomalies to cohomology and demonstrating numerical detection methods for symmetry-protected order.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Topological Phases of Matter
Background:
- Edge theories of topological phases often display global symmetry anomalies.
- Understanding these anomalies is crucial for characterizing topological phases.
Purpose of the Study:
- To analyze edge anomalies in two-dimensional bosonic symmetry-protected topological phases.
- To connect physical interpretations of anomalies (orbifolding, boundary construction) with cohomology classification.
- To develop numerical methods for detecting symmetry-protected order.
Main Methods:
- Focus on two-dimensional bosonic phases with on-site symmetry.
- Utilize tensor network and matrix product state formalisms for numerical analysis.
- Investigate connections between anomalies, orbifolding, and symmetry-preserving boundaries.
Main Results:
- Detailed analysis of edge anomalies in the studied phases.
- Demonstration of how anomalies relate to obstructions in constructing symmetry-preserving boundaries.
- Numerical illustration of the theoretical arguments using tensor networks.
Conclusions:
- Edge anomalies provide key insights into the nature of symmetry-protected topological phases.
- The study offers a framework for understanding and computationally detecting symmetry-protected order.
- The findings bridge theoretical classification with numerical simulation in condensed matter systems.
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