1989 Fiscal Year Final Research Report Summary
Research on Finite Quantum Spin Systems
| Project/Area Number |
62540261
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Nagaoka University of Technology |
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Principal Investigator |
OGUCHI Takehiko Nagaoka Univ. of Technology, Department of Sciences and Mathematics, Professor., 工学部, 教授 (70016137)
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| Co-Investigator(Kenkyū-buntansha) |
KITATANI Hidetsugu Nagaoka Univ. of Technology, Department of Sciences and Mathematics, Research As, 工学部, 助手 (70186245)
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| Project Period (FY) |
1987 – 1989
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| Keywords | Quantum spin systems / Heisenberg model / Resonating valence bond / Ising model / Transfer matrix method / Finite-size scaling / Triangular lattice / Coherent-anomaly method |
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| Research Abstract |
1) Two new methods have been proposed to caluculate physical quantities. In both methods, the systems divided into several subsystems, so that we can fairly decrease the storage of computer. Therefore, we can deal with large systems which are so large that direct diagonalization is not possible. The first method is the application of Trotter-formulae and the second one is that of the peiturbational method.
2) Several properties of eigenvalues and eigenfunctions for finite antiferromagnetic Heisenberg model have been rigorously proved. One of the results is that the parity of the ground state is even for N=4,8,12,...and odd for N=2,6,10...(N is the total number of spins).
3) The theory of the resonating valence bond(RVB) for the antiferromagnetic Heisenberg model of spin 1/2 proposed by Anderson is generalized. It has been shown that the ground state of the system is represented by singlet bonds which connect not only nearest but also distant spins.
4) The correlation functions, the value of eta of paramagnetic-spin glass phase transition have been calculated by using screw transfer matrix methods.
5) The coherent-anomaly method is applied to the spin 1/2 ferromagnetic Heisenberg model to estimate the critical exponents.
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