2020 Fiscal Year Research-status Report
Topological aspects of quantum many-body systems: Symmetry-protected ingappable phases and anomalies
| Project/Area Number |
19K14608
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| Research Institution | Institute of Physical and Chemical Research |
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Principal Investigator |
Hsieh ChangTse 国立研究開発法人理化学研究所, 創発物性科学研究センター, 基礎科学特別研究員 (70822146)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | Quantum criticality / Conformal field theory / Majorana fermions / Quantum spin chains |
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| Outline of Annual Research Achievements |
1. In the work "Fermionic Minimal Models" (published in Physical Review Letters recently), we discovered a new family of universality classes, described by a fermionic extension of the Virasoro minimal models of 2d conformal field theories, in 1+1d quantum systems of Majorana fermions. This broadens people's current understanding of critical phenomena in fermionic systems. Besides providing the theoretical basis of such fermionic minimal models, our technique of constructing explicit Hamiltonians realizing these theories should also be useful, especially for model building, and hence our study can motivate further research along this direction, i.e. on fermionic quantum criticality.
2. The principal investigator was recently awarded the 15th (2021) Young Scientist Award of the Physical Society of Japan (awarded to young researchers who have made outstanding achievements in their early research careers) in theoretical particle physics.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
In addition to works directly related to the research proposal, I have also been working on other topics inspired by and extended from the original plan, such as studies of topological responses of topological crystals and critical phenomena of non-Hermitian quantum systems, and have made significant progress.
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| Strategy for Future Research Activity |
1. Extend the study of fermionic minimal models in 1+1 dimensions, including finding an effective Landau-Ginzburg description of such theories and the precise connection between primary fields and their lattice counterparts by the approach of e.g. tensor network.
2. Obtain a topological response theory of a crystalline symmetry protected topological phases from the topological crystal picture.
3. Construct a mapping between Hermitian and non-Hermitian systems to study the connection between their associated phases and phase transitions.
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