Geometrical phases by Majorana representation and topological order parameters
| Project/Area Number |
25610101
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Keywords | 幾何学的位相 / ベリー接続 / トポロジカル秩序 / エンタングルメントチャーン数 / マヨラナ表示 / トポロジカル相 / BdG方程式 / 量子エンタングルメント / ベリー位相 / ボゴリューボフ・ドジャンハミルトニアン |
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| Outline of Final Research Achievements |
Topological material is a class of novel phases of matter where any of symmetry breaking is not crucially important for the classification. As for such topological phases, we have constructed series of topological order parameters using geometrical phases such as the Chern numbers and Berry phases. Here in this project, we have investigated a Majorana representation of fermions in relation to the Berry connection to define novel topological order parameters. Then we have developed a theoretical framework for the Bogoliubov-de Gennes equation.
Through the theoretical trials, we have noticed and found an advantage of the quantum entanglement for the characterization. Then we have defined an entanglement Chern number and entanglement Berry phases associated with an extensive partition using a purification of the entanglement Hamiltonian.
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Report
(3 results)
Research Products
(42 results)
