2023 Fiscal Year Final Research Report
Interacting topological phases and operator algebras
| Project/Area Number |
19K14548
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Nagoya University (2023)
Tohoku University (2019-2022) |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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| Keywords | Topological phase / Operator algebras / Index theory / 作用素環論 / トポロジカル相 / 指数理論 |
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| Outline of Final Research Achievements |
The project was an exploration of topological properties of gapped ground states. That is, properties of low-energy quantum mechanical systems which are stable under small perturbations and deformations. Our primary method for studying such problems was to use methods from operator algebras and non-commutative index theory.
Homology and cohomology are mathematical tools that give a simple algebraic description of a potential complicated setting (for example, how many holes in a shape). By using homology and cohomology theories for operator algebras, which describe quantum mechanical systems, we mathematically characterised stable properties of a wide variety of gapped ground states.
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| Free Research Field |
作用素環論
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| Academic Significance and Societal Importance of the Research Achievements |
Ground states give the most basic information about quantum mechanical system. By understanding the topological properties of ground states, we can understand which systems can be loosely connected and which are manifestly distinct. This aids our conceptual understanding of materials.
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