Use of quaternions for topological phases: many body problem and time reversal symmetry breaking
| Project/Area Number |
16K13845
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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) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 四元数 / 時間反転対称性 / クラマース縮退 / ベリー接続 / 電子間相互作用 / 時間反転対称性の破れ / 対称性の破れ / エンタングルメント / 磁場 / 擬ポテンシャル / 平坦バンド / 多体問題 / ラフリン状態 |
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| Outline of Final Research Achievements |
As for a fermionic system with time-reversal invariance, Any one particle state is inevitably degenerate with some other state this is known as the Kramers degeneracy. Combining the Kramers pair with a suitable phase, one obtains a quaternionic wave function. This is an idea of the applicant. Also the Berry connection has been quite useful for a study of topological phases as in the case of the quantum Hall effects. Then the quaternionic Berry connection is useful for the study of topological phases with time-reversal invariance.
Based on the facts, we have tried to use a quaternionic representation for the time-reversal symmetric systems with electron-electron interaction and also discuss effects of weak time-reversal symmetry breaking.
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| Academic Significance and Societal Importance of the Research Achievements |
時間反転対称なフェルミオン系のハミルトニアンが四元数表示されることはDyson以来のよく知られた事実であるが，そのクラマース縮退した波動関数を組み合わせることで波動関数を四元数とできることは申請者の独自の発案であり，この手法をトポロジカル相に対するベリー接続の理論として適用し，電子間相互作用を議論することならび時間反転対称性の破れを議論することは新しい展開をもたらし，学術的意義は大きい。また，四元数という基本的で有用な概念を広く普及するという社会的な意義もある。
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Report
(4 results)
Research Products
(124 results)
