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Categorical Landau Paradigm for Gapped Phases.
Lakshya Bhardwaj1, Lea E Bottini1, Daniel Pajer1
1University of Oxford, Mathematical Institute, Woodstock Road, Oxford, OX2 6GG, United Kingdom.
Physical Review Letters
|November 1, 2024
Summary
We introduce a unified framework for classifying gapped phases with categorical symmetries, extending the Landau paradigm. This approach utilizes symmetry topological field theory for comprehensive phase classification across dimensions.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Topological Phases of Matter
Background:
- Gapped phases of matter with symmetry are fundamental in condensed matter.
- Existing classification schemes can be complex and limited in scope.
- Categorical symmetries offer a richer mathematical structure for describing phases.
Purpose of the Study:
- To develop a unified and comprehensive framework for classifying gapped phases with categorical symmetries.
- To generalize the Landau paradigm to incorporate categorical symmetries.
- To provide a computationally powerful approach for phase classification.
Main Methods:
- Proposing a unified framework based on symmetry topological field theory (TFT).
- Utilizing a one-dimension higher TFT with topological boundaries.
- Illustrating the framework for (1+1)-dimensional gapped phases with categorical symmetries.
Main Results:
- A generalized, categorical Landau paradigm for classifying gapped symmetric phases.
- The framework is applicable in any dimension.
- Demonstration of the approach for (1+1)D systems.
Conclusions:
- The proposed framework offers a succinct, comprehensive, and computationally powerful method for classifying gapped symmetric phases.
- Symmetry TFT provides a powerful tool for understanding topological phases.
- The framework has potential for higher-dimensional extensions and further theoretical development.
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