Numerical Study of the Ground States of the Low Dimensional Quantum Heisenberg Models
| Project/Area Number |
07640503
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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 |
物性一般(含基礎論)
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| Research Institution | Saitama University |
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Principal Investigator |
HIDA Kazuo Saitama University Faclty Science, Department of Physics Associated Professor, 理学部, 助教授 (20133704)
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| Project Period (FY) |
1995 – 1997
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| Project Status |
Completed (Fiscal Year 1997)
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| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1997: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1996: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1995: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | quantum Heisenberg model / spatial structure / random / spin gap state / numerical diagonalization / density matrix renormalization group / quantum Monte Carlo / dimer expansion / ランダム量子ハイゼンベルグモデル / ボンド交替 / ランダムシングレット相 / 大スピン相 / ランダムダイマー相 / ストリング秩序 / 実空間繰り込み群 / 量子悌子ハイゼンベルグモデル / 2層J-_1-J_2モデル / ランダム量子ハイゼンベルフモデル / 修正スピン波近似 / フラストレーション / 量子スピン液体 / スケーリング |
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| Research Abstract |
In this 3-year project, the low dimensional quantum Heiscnberg models with various spatial structures have been investigated using numerical methods. The main results are summarized as follows :
1.The critical behavior of the ladder quantum Heisenberg model is studied in the limit of weak interchain interaction using the density matrix renormalization group (DMRG) method.
2.The algorithm of the DMRG method for one-dimensional random quantum systems is developed. The existence of the random singlet phase is verified in the random antiferromagnetic quantum Heisenberg model. The application to the quasi-periodic systems is in progress.
3.The low energy behavior of the one-dimensional random quantum antiferromagnetic Heisenberg model in the presence of the ferromagnetic bonds is investigated using the DMRG method. The temperature dependence of the specific heat and magnetic susceptibility is discussed.
4.The one-dimensional random quantum antiferromagnet with bond alternation is studied using
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the DMRG method. the bond-alternation-dependence of the grund state energy, gap distribution and the string order is obtained. It is shown that the spin-Peierls instability is suppressed by randomness.
5.The finite temperature magnetization process of the one-dimensional ferromagnetic-antiferromagnetic alternating Heisenberg model is investigated using the quantum Monte Carlo method and the mapping onto the one-dimensional boson system.
6.The ground state of the isotropic one-dimsnaional Heisenberg model with 2 and 4-fold spatial periodicity is investigated using the exact numerical diagoualization method. The phase diagram and the critical exponents are calculated. The relationship between the dimerization transition of the spin-1/2 antiferromagnetic Heisenberg chain and the Haldane-dimer transition of the spin-1 antiferromagnetic Heisenberg chain is clarified. The study of the effect of the anisotropy and magnetic field is in progress.
7.The effect of frustration on the ground state and excitation spectrum of the spin-1/2 bilayr quantum antiferromagnetic Heisenberg model is studied using the modified spin wave method and the dimer expansion method. It is found that the spin gap state survives down to the limit of weak interlayr coupling. Less
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Report
(4 results)
Research Products
(23 results)
