Geometrical Phases in Condensed Matter Theory : Qutnaum Phase Transition and Classification by topological orders
| Project/Area Number |
17540347
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 |
HATSUGAI Yasuhiro The University of Tokyo, Applied Physics, Associate Professor (80218495)
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| Co-Investigator(Kenkyū-buntansha) |
RYU Shinsei University of Tokyo, Applied Physics, Research Associate (90376492)
MARUYAMA Isao University of Tokyo, Applied Physics, Research Associate (20422339)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2006: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2005: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | Topological orders / Quantum liquids / Berry phases / Quantum Orders / Entanglement entropy / Time reversal Symmetry / Symmetry breaking / Order parameter / 幾何学的位相 / 量子化 / 強相関電子系 / エンタングルメントエントロピ / 量子相転移 / ベリー接続 / フラストレーション / ダイマー / 時間反転 |
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| Research Abstract |
There is a fundamental class of many-body quantum states that do not possess relevant symmetry breaking. It includes quantum Hall states, anisotropic superconductors, graphene, Kondo insulators, quantum spins with frustrations and so on. In these low dimensional systems, strong quantum fluctuations prevent from developing classical order characterizing the states. These are quantum liquids where the quantum effects themselves are their characteristic features. Assuming the state is gapped, we characterized the quantum ground state without symmetry breaking by defining a topological local order parameter. It is defined by a quantized Berry phase where some anti-unitary symmetry such as time reversal or particle-hole guarantee the quantization of the Berry phase. This topological order parameter is quite useful to describe quantum phase transitions where the symmetry of the system remains the same. We also characterized the state by the uses of an entanglement entropy for the these quantum phase transition of the gapped quantum liquids based on the bulk-edge correspondence. We have successfully developed our original theory and show their validity by application to many concrete systems.
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Report
(3 results)
Research Products
(78 results)
