Theoretical Studies of Low Dimensional Quantum Magnets with Spatial Structures

1.研究了S=1 kagome Heisenberg反铁磁体中由于晶格形变和各向异性引起的量子相变。结果表明，未变形的各向同性系统的基态是本文提出的HSS-态。2.确定了一维S=1 XXZ模型的定量精确的基态相图。虽然目前的结果在质量上并不新颖，3.利用密度矩阵重整化群方法研究了锯齿键混合海森堡链和强键随机被铁磁键取代的锯齿键海森堡链在饱和磁化强度一半时的平台行为用DMRG方法研究了反铁磁交替键链和均匀键链混合物的非对称性。结果表明，实验磁化强度随温度的升高而增大， ...更多信息 用真实的空间重整化群方法重新研究了Fibonacci反铁磁XXZ模型在两种交换作用的大小相差很大的情况下的基态.得到了基态相图，并表明了新普适类的存在。6.将键算符平均场方法应用于一维锯齿形交替键链的m=1/3平台态，重现了利根川等人得到的相图，并研究了链间相互作用的影响。7.在周期为-3S =1/3的M=1/3平台中，2 zigzag Heisenberg模型，结果表明经典平台态和量子平台态是不同的相，存在一个Z_2对称性破缺的中间相。8.利用数值对角化方法研究了具有空间调制单离子各向异性D的S[大于或等于]1海森堡链。结果表明，随着空间调制模式的变化，出现了各种反铁磁相和亚铁磁相。9.在磁场中的准一维量子磁体中，随机性一方面使自旋复活，另一方面诱导出横向磁序。另一方面，它导致了随机诱导平台，破坏了磁有序。由于这两种机制的竞争，结果表明，随着磁场的增加，该系统经历了多次重入相变。少

1.The quantum phase transitions due to lattice deformation and anisotropy in the S=1 kagome Heisenberg antiferromagnet are investigated. It is shown that the ground state of the undeformed isotropic system is the HSS-state proposed by the present head investigator.2.The quantitatively accurate ground state phase diagram of the one-dimensional S=1 XXZ model is determined. Although the present result is not qualitatively new, it will serve as a standard in this field due to its quantitative accuracy.3.The behavior of the plateau at the half of the saturation magnetization is investigated using the density matrix renormalization group method for the mixed zigzag bond Heisenberg chain and zigzag bond Heisenberg chain in which the strong bonds are randomly replaced by the ferromagnetic bonds.4.The magnetization process of the mixture of the antiferromagnetic alternating bond chain and the uniform chain is investigated using the DMRG method. It is shown that the experimental magnetization cu … More rve obtained by Ajiro and workers is explained results.5.The ground state of Fibonacci antiferromagnetic XXZ model is re-investigated using the real space renormalization group method in the case where the magnitudes of the two exchange interactions are largely different. The ground state phase diagram is obtained and the presence of new universality class is shown.6.The bond operator mean field method is appled to the m=1/3 plateau state of the one-dimensional zigzag alternating bond chain to reproduce the phase diagram obtained by Tonegawa et al. The effect of the interchain interaction is also investigated.7.Among the M=1/3 plateaus of the period-3 S=1/2 zigzag Heisenberg model, it is shown that the classical plateau state and quantum plateau state are different phases and that there exists an imtermediate phase with Z_2 symmetry breakdown. The model with 4-spin interaction with the quantum plateau ground state is also constructed.8.The S【greater than or equal】1 Heisenberg chain with spatially modulated single ion anisotropy D is investigated by numerical diagonalization. It is shown that various antiferromagnetic phases and ferrimagnetic phases appear according to the pattern of the spatial modulation.9.In quasi-one-dimensional quantum magnets in the magnetic field, randomness revives the spins and induces the transverse magnetic order on the one hand. On the other hand, it induces the randomness induced plateau and destroys the magnetic order. As a result of the competition of these two mechanisms, it is shown that this system undergoes multiple reentrant phase transitions with the increase of the magnetic field. Less