2018 Fiscal Year Final Research Report
Probing topological phases through the global properties of their wave functions
| Project/Area Number |
15K05224
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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 | National Institute for Materials Science |
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Principal Investigator |
Tanaka Akihiro 国立研究開発法人物質・材料研究機構, 国際ナノアーキテクトニクス研究拠点, グループリーダー (10354143)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | トポロジカル物質相 / 波動関数の大域挙動 / トポロジカル作用項 / 量子数の分数化 / Lieb-Schultz-Mattisの方法 |
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| Outline of Final Research Achievements |
A large number of topological phases of matter exhibit a characteristic surface effect: the emergence of a gapless and protected surface state. Here we have demonstrated that by starting with low-energy effective theories featuring a topological term and utilizing the imaginary-time ppath-integral framework, we encounter a closely related surface effect which takes place at the time slice situated at the teminal point of the imaginary time evolution.This surface effect induces a topological phase factor into the ground state wave function, which in turn governs the global behavior of the system. We succesfully applied this "temporal bulk-boundary correspondence" to (1) the evaluation of the etanglement spectrum (2) the evaluation of the so-called strange correlator first suggested by C.-K. Xu's group (3) a field-theory version of the Lieb-Schultz-Mattis argument.
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| Free Research Field |
物性物理学
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| Academic Significance and Societal Importance of the Research Achievements |
トポロジカル絶縁体や，その先駆けに当たる量子スピン鎖のハルデーン状態は，系の端や境界に特徴的なギャップレス状態が現れることが広く知られる．本課題では同様の「表面効果」が空間方向のみならず時間方向にも表れ，基底状態の波動関数を支配することを示した．最も直近の成果としては，基底状態近傍の励起状態も同様に構成できること（エネルギーギャップの有無，トポロジカル秩序の有無の問題と直結）が判明した．具体的には量子スピン系や時間反転対称性なトポロジカル絶縁体を対象としたが，スキームは原理的にはより広範な問題へと適用できるものであり，場の理論的に基づく有効なアプローチとして一定の意義があるものと考えられる．
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