2001 Fiscal Year Final Research Report Summary
Theoretical and Numerical Study of Many-Body Interaction and Quantum Phase Transition in Low-Dimensional Magnets
| Project/Area Number |
11440103
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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 |
固体物性Ⅱ(磁性・金属・低温)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TAKAHASHI Minoru Institute for Solid State Physics, Professor, 物性研究所, 教授 (40029731)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAI Toru Tokyo Metropolitan Institute of Technology Faculty of Engineering, Associate Professor, 工学部, 助教授 (60235116)
SHIROISHI Masahiro Institute for Solid State Physics, Research Associate, 物性研究所, 助手 (80323632)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Magnetization Curve / Magnetic Plateau / Low-Dimensional Systems / Spin Systemes / Exact Solution / Bethe ansatz / Thermodynamics / Exact diagonalization |
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| Research Abstract |
1) High temperature expansion of XXX model by new integral equation
High temperature expansion of thermodynamic quantities such as specific heat and magnetic susceptibility for one-dimensional Heisenberg model has been done up to 24-th order using finite cluster method. On the other hand high temperature expansion by Bethe ansatz method was believed to be difficult. But we succeeded to expand to 100th order using new thermodynamic Bethe ansatz equation. We apply Pade approximation and compared with the numerical results of quantum transfer matrix method.
2) Comparison of Bethe ansatz equation with high-temperature expansion for Hubbard model
Thermodynamic Bethe ansatz equation has infinite number of unknown functions. We made cut off and used Newton's method to solve non-linear integral equation. Generally speaking thermodynamic quantities are expressed by the differentiation of grand potential. Then we must solve linear integral equation to get thermodynamic quantities. But this equation can be done in the same method in Newton's method. Only by one time linear operation we can get first order thermodynamic quantities such as energy, entropy, magnetization and particle density.
3) Emptiness formation probability of one-dimensional isotropic XY model
We investigated the emptiness formation probability which is one of many points corellation functions for one-dimensional XY model using numerical and analytical methods
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