Theoretical Studies of Low Dimensional Quantum Magnets with Spatial Structures

1.一维随机量子磁体利用密度矩阵重整化群（DMRG）方法，我们证明了自旋为1的一维Heisenterg反铁磁体的Half态是抗随机稳定的.利用DMRG方法研究了自旋为1/2的一维准周期反铁磁XXZ模型的基态。结果表明，XY模型中的Fibonacci调制在反铁磁Ising相互作用的存在下变得相关，并且低能行为被显著地改变.利用DMRG和微扰重整化群方法研究了一维半填充Fibonacci Hubbard模型.结果表明，即使在半填充的情况下，也可以实现多种基态。这些阶段的实验观察，预计使用量子点阵列和其他系统。我们的结果表明了强关联效应在准周期系统中的重要性. 关于我们 具有长空间周期性的一维量子磁体利用精确对角化方法，研究了各种具有长空间周期性的一维量子磁体的基态和磁化过程，明确了量子相变的普适类和临界指数. Kagome晶格量子反铁磁体用精确对角化和集团展开方法研究了在有机材料中实现的自旋为1的Kagome反铁磁体的基态和低能激发态光谱。结果表明，磁性和非磁性激发都有有限的能隙。提出了六角单重态立体图，其中的挫挫被量子涨落完全补偿。在全磁化的1/3处出现一个磁化平台。未来的研究项目同一课题的研究项目已获批准，以下研究正在进行中。(1)随机一维量子磁体的磁化过程（2）kagome反铁磁体的有限温度性质（3）S=1的一维单格点各向异性XXZ模型的基态相图（4）用键算符方法研究准一维和准二维量子磁体的磁化平台

1. One-dimensional random quantum magnetsUsing the density matrix renormalization group (DMRG) method, we have shown that the Haldane state in spin-1 1-dimensional Heisenterg antiferromagnet is stable against randomness.2. One-dimensional quasiperiodic quantum magnetsUsing DMRG, the ground state of spin-1/2 1-dimensional quasipenodic antiferromagnetic XXZ model is investigated. It is shown that the Fibonacci modulation, which is critical in the XY model, becomes relevant in the presence of the antiferromagnetic Ising interaction and the low energy behavior is modified drastically.The one-dimensional half-filled Fibonacci Hubbard model is investigated using DMRG and perturbational renormalization group method. It is shown that a varity of ground states are realized even in the half-filled case. Experimental observation of these phases is expected using the quantum dot array and other systems. Our results suggest the importance of the strong correlation effect in quasiperiodic systems.3. … More One-dimensional quantum magnets with long spatial periodicityUsing the exact diagonalization method, the ground state and magnetization process of various one-dimensional quantum magnets with long spatial periodicity are investigated and universality class and critical exponents of quantum phase transition are clarified.4. Kagome lattice quantum antiferromagnetGround state and low energy exciatation spectrum of the spin-1 kagomee antiferromagnet which is realized in an organic material are investigated by the exact diagonalization and cluster expansion method. It is shown that both magnetic and non-magnetic excitations have finite energy gaps. The hexagonal singlet solid picture is proposed in which the frustration is fully compensated by quantum fluctuation. It is also shown that a magnetization plateau appears at 1/3 of full magnetization.Future projectsThe project with the same subject is approved and the following investigations are in progress.(1) Magnetization process of random one-dimensional quantum magnets(2) Finite temperature properties of the kagome antiferromagnets(3) Ground state phase diagram of S=1 1-dimensional XXZ model with single-site anisotropy(4) Studies of magnetization plateaux in quasi-1-dimensional and quasi-2-dinensional quantum magnets using the bond operator method Less