| Project/Area Number |
25400407
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Gakushuin University |
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Principal Investigator |
Tasaki Hal 学習院大学, 理学部, 教授 (50207015)
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| Co-Investigator(Kenkyū-buntansha) |
Tanaka Akinori 有明工業高等専門学校, 准教授 (80274512)
Katsura Hosho 東京大学, 理学系研究科, 准教授 (80534594)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 数理物理 / 量子多体系 / 強相関電子系 / ハバード模型 / 金属強磁性 / マヨラナ端状態 / 朝永・ラッティンジャー液体 / 磁気秩序 / トポロジカル相 / 正弦 2 乗変形 / エンタングルメントエントロピー / 超伝導 / マヨラナフェルミオン系 / キンク解 / 緩和現象 / 冷却原子系 / ボース・ハバード模型 |
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| Outline of Final Research Achievements |
The aim of the project had been to elucidate nontrivial orders and phase structures which emerge in strongly interacting many-body quantum systems, and, at the same time, to develop novel mathematical methods based on physical pictures and points of view. The most important achievement was a theorem which established the emergence of metallic ferromagnetism in the Hubbard type model which represents physically natural situation that "strong repulsion between electrons in a single band leads to ferromagnetic order". Notably a new mathematical method, especially suited for the study of metallic ferromagnetism, had been developed in this study. There was also progress in the researches of ferromagnetsim in a gapless multi-band Hubbard model, the emergence of Majorana edge states in some strongly interacting electron systems, and the Tomonoga-Luttinger liquid in the Bose-Hubbard models with flat-bands.
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