2010 Fiscal Year Final Research Report
Infinite-dimensional symmetry of exactly solvable models and various physical applications in the finite-size quantum many-body systems
| Project/Area Number |
20540365
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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 | Ochanomizu University |
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Principal Investigator |
DEGUCHI Tetsuo Ochanomizu University, 大学院・人間文化創成科学研究科, 教授 (70227544)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 可積分系 / 数理物理 / 無限次元対称性 / べーテ仮説 / 量子XXZ鎖 / 可解な高次スピン量子スピン鎖 / 相関関数 / 1次元デルタ関数型相互作用ボソン |
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| Research Abstract |
Applying the infinite-dimensional symmetries of quantum integrable systems, we derive exactly various interesting physical properties of large but finite-size quantum integrable systems. For instance, through the sl (2) loop algebra, which is an infinite-dimensional Lie algebra appearing in the XXZ spn chain when q is a root of unity, we classify the Hilbert space of the super-integrable chiral Potts model and derive the eigenvectors, explicitly. Making use of the asymmetric R-matrix of the XXZ spin chain, we derived the multiple-integral representations of arbitrary correlation functions.
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