2000 Fiscal Year Final Research Report Summary
Theoretical Study on Quantum Phase Transitions by the Density Matrix Renormalization Group Method
| Project/Area Number |
10640330
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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 |
固体物性Ⅱ(磁性・金属・低温)
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| Research Institution | University of Tokyo |
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Principal Investigator |
UEDA Kazuo University of Tokyo, Institute for Solid State Physics, Professor, 物性研究所, 教授 (70114395)
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| Project Period (FY) |
1998 – 2000
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| Keywords | Field induced gap / Sine-Gordon field theory / Dzyaloshinskii-Moriya interaction / Density matrix renormalization group / Spin gap / Charge ordering / Orthogonal dimer / Triplet excitations |
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| Research Abstract |
Yb_4As_3 had been known as a Kondo system with small density of carriers. However, Prof. Fulde and coworkers proposed that the one-dimensional spin chains formed by the charge ordering is responsible for the specific heat linear in T.This proposal was confirmed by the neutron scattering measurements by Prof. Kohgi's group. However, still the phenomena of opening of a gap in magnetic fields remained as an open question. We analyzed the structure of Yb_4As_3 and pointed out that the Dzyaloshinskii-Moriya interaction is responsible for the formation of the spin gap. Further we derived the effective Hamiltonian for the spin chains which naturally contains the Dzyaloshinskii-Moriya interaction. The low energy effective theory for the system is the Sine-Gordon field theory. However, in order to understand the physics in the entire energy range, the density matrix renormalization group is the most reliable method and investigations under this direction is now under way.
Concerning the orthogonal dimer system realized in SrCu_2(BO_3)_2, two triplet excitations were investigated by using a perturbative approach. It has been shown that the dispersion for the higher triplet branch due to the two-triplet excitations has a wider dispersion than the lowest one.
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