2009 Fiscal Year Final Research Report
Correlation functions of solvable models and thermal transport phenomena
| Project/Area Number |
18340112
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 |
TAKAHASHI Minoru The University of Tokyo, 理学部, 訪問教授 (40029731)
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| Co-Investigator(Kenkyū-buntansha) |
SHIROISHI Masahiro 東京大学, 物性研究所, 助教 (80323632)
SAKAI Kazumitsu 東京大学, 総合文化研究科, 助教 (10397028)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 可積分系 / 磁性 / 数理物理 / 統計力学 / 低次元系 / 相関関数 / 熱力学 |
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| Research Abstract |
・ Static correlation functions of one dimensional XXX and XXZ models at the ground state Before this project we already calculated 4-th neighbor correlation functions. We invented the generating functions method and could calculate fifth, sixth and seventh correlation functions. Moreover we calculated density submatrix of successive seven cites.
・ Thermodynamics of solvable models
Takahashi proposed new type of thermodynamic Bethe ansatz equation for 1D XXZ model in 2001. Same type of equations are derived for more complicated models like Uimin-Sutherland model and Perk-Schultz model. We give the high temperature expansion of thermodynamic quantities (specific heat, magnetic susceptibility, etc). We treated the thermodynamic problem of one dimensional bosons which has spin.
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