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Unveiling correlated two-dimensional topological insulators through fermionic tensor network states-classification,
Chao Xu1, Yixin Ma1, Shenghan Jiang1
1Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
Reports on Progress in Physics. Physical Society (Great Britain)
|August 16, 2024
Summary
This study introduces a new framework for simulating topological insulators in strongly correlated systems using fermionic tensor network states. It enables the creation of variational wave functions for these complex materials, advancing simulation capabilities.
Area of Science:
- Condensed Matter Physics
- Quantum Materials Science
Background:
- Topological band insulators exhibit unique properties like band topology indices and protected boundary modes.
- In strongly correlated systems, traditional band theory fails, yet topological insulator phases remain distinct from trivial insulators.
Purpose of the Study:
- To develop a general framework for fermionic tensor network states to simulate topological insulator phases in strongly correlated systems.
- To formulate generic variational wave functions for numerical simulations where Slater determinants are not applicable.
Main Methods:
- Developed a comprehensive framework for fermionic tensor network states tailored for two-dimensional topological insulators.
- Derived sets of tensor equations representing symmetry transformation rules for various symmetry groups.
- Constructed edge theories and extracted quantum anomaly data to classify non-chiral topological insulator phases.
Main Results:
- Achieved a systematic classification of non-chiral topological insulator phases by exploring all possible tensor equation sets.
- Generated generic variational wave functions by applying solutions of tensor equations to local tensors.
- Established a connection between tensor equations, edge theories, and quantum anomaly data.
Conclusions:
- The developed methodology is a significant step towards simulating topological insulators in strongly correlated systems.
- The framework provides a pathway for creating accurate variational wave functions for complex quantum materials.
- Further advancements are anticipated through exploring limitations and potential generalizations of the current approach.
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