Theoretical Research of Quantum Spin Systems with Spin Gap

点击翻译按钮获取中文摘要

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 one-dimensional 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 model-dependent. The topological term determines whether the system has a spin gap or not. From the topological term we derived the gapless equations for various period-4 spin systems and obtained ground-state phase diagrams. For each phase we qualitatively explained the ground-state wave-function by the singlet-cluster-solid 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)_2-2H_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.