Classification of Phases in Strongly Correlated Quantum Many-Body Systems and Quantum Anomaly in Field Theory
| Project/Area Number |
16K05469
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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 | The University of Tokyo |
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Principal Investigator |
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| Research Collaborator |
FURUYA Shunsuke
YAO Yuan
HSIEH Chang-Tse
KOBAYASHI Ryohei
FUKUSUMI Yoshiki
NAKAGAWA Yuya O.
WATANABE Haruki
FUJITA Hiroyuki
SUGIURA Sho
LU Yuan-Ming
RAN Ying
MISGUICH Gregoire
PASQUIER Vincent
LO Chung-Yu
KAO Ying-Jer
CHEN Pochung
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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 |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | 量子多体系 / 量子異常 / 量子臨界状態 / 電気分極 / 有限サイズスケーリング / 量子相 / 量子臨界現象 / Lieb-Schultz-Mattis定理 / 量子ホール効果 / 量子スピン鎖 / SU(N)対称性 / 物性基礎論 / 場の理論 / 統計力学 / 反強磁性体 / 数理物理 / 物性理論 |
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| Outline of Final Research Achievements |
Gapless states, in which the ground state can be modified by an infinitesimal energy, appear not only at quantum phase transition, but also as stable quantum critical phases. In this project, we introduced two novel characterizations of gapless quantum critical states. One is a quantum anomaly, which represents an obstruction against gauging (localizing) both the spin rotation symmetry and translation of spin locations simultaneously. The second is a new exponent characterizing the scaling of the polarization amplitude, which represents the magnitude of the fluctuations of the electric polarization, when the system size is increased.
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| Academic Significance and Societal Importance of the Research Achievements |
ギャップレスな量子臨界状態の理論的・数値的解析はギャップのある相に比較して難しく、未開拓の部分がかなり大きい。本研究で、場の理論において重要な概念である量子異常、また物理的に自然かつ重要な概念である電気分極に基づいて、ギャップレスな量子臨界状態の新たな視点からの分類を行ったことは、ギャップレスな量子臨界状態の包括的な理解に向けた一歩である。実際、本研究を受けて、ギャップレスな量子臨界状態の分類の理論がさまざまな観点から盛んになっており、このような世界的な研究の潮流を作り出す一つの契機を与えた先導的な研究成果であると考えている。
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Report
(4 results)
Research Products
(39 results)
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[Presentation] Polarization and Gauge Invariance2016
Author(s)
Masaki Oshikawa
Organizer
BIRS Workshop "Geometrical Degrees of Freedom in Topological Phases"
Place of Presentation
Banff International Research Station, Banff, Canada
Year and Date
2016-08-21
Related Report
Int'l Joint Research / Invited
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