Project/Area Number  10640357 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
固体物性II(磁性・金属・低温)

Research Institution  Toyota Technological Institute 
Principal Investigator 
TAKANO Ken'ichi Toyota Technological Institute, Department of Advanced Science and Technology, Associate Professor, 工学部, 助教授 (00197112)

CoInvestigator(Kenkyūbuntansha) 
SANO Kazuhiro Mie University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (40201537)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2000)

Budget Amount *help 
¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 2000 : ¥300,000 (Direct Cost : ¥300,000)
Fiscal Year 1999 : ¥300,000 (Direct Cost : ¥300,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)

Keywords  spin gap / mixed quantum spin system / Heisenberg model / nonlinear σ model / onedimensional system / disordered state / singlet cluster / diamond chain / スピン・ギャップ / 混合量子スピン系 / ハイゼンベルク模型 / 非線型シグマ模型 / 1次元系 / 無秩序状態 / シングレット・クラスター / ダイヤモンド鎖 / ハイゼンベルグ模型 / ダイヤモンド型格子 / 非線形シグマ模型 / 量子スピン系 / 反強磁性 / 2次元 / CaV_4O_9 
Research Abstract 
Under strong quantum fluctuation by low dimensionality or frustration, a quantum spin system may have a disordered ground state and a finite spin excitation gap. We examined properties of the disordered state and the origin of the spin gap, and tried to clarify effects of quantum fluctuation in such systems. We found a general method to derive the nonlinear σ model representing a onedimensional mixed quantum spin system. Almost methods before the present are not justified because the degrees of freedom change in the process of transformation, and also are modeldependent. The topological term determines whether the system has a spin gap or not. From the topological term we derived the gapless equations for various period4 spin systems and obtained groundstate phase diagrams. For each phase we qualitatively explained the groundstate wavefunction by the singletclustersolid picture. As spin models with strong frustration, we examined the distorted diamond chain and are regularly depleted square lattice. Candidates for the models were Cu_3Cl_6(H_2O)_22H_8C_4SO_2. and CaV_4O_9 respectively. We numerically diagonalized the spin models, analyzed experimental data, and compared them. We particularly estimated the values of the exchange interactions and analyzed the origins of the spin gaps of these materials. As a result, we found that other effects rather than frustration are strong in these materials. Through this research project we have obtained concrete knowledge about various quantum spin systems which have strong quantum fluctuation, and clarified conditions for the spin gap formation. There are ground states with spin gap which cannot transform continuously to each other. We have also constructed a nonlinear σ model method which is general, reasonable and further developable.
