Theoretical study of one-dimensional quantum spin systems in which two kinds of spins with different magnitudes are regularly arranged

我们研究了以下两种规则混合量子自旋链的基态：两个S=1/2和两个S=1自旋交替排列的自旋-1/2-1/2-1-1链在交换相互作用常数平面上的基态相图，其中S=1自旋之间的交换相互作用为反铁磁性的。采用基于Lieb-Mattis定理和Wigner-Eckart定理的解析方法以及有限大小系统的精确对角化方法和密度-矩阵重整化群（DMRG）方法等数值方法。我们还计算了基态的双自旋相关函数和弦序参数，并给出了相的表征，即如何在价键-固体（VBS）图的框架中表示每个相的基态。结果表明，在基态图中出现的11个相中，有5个相具有二聚体特征，其余6个相具有霍尔丹特征。此外，我们还研究了S=1自旋的单轴单离子型各向异性对自旋-1/2-1/2-1-1链基态的影响。应用现象学重整化群（PRG）方法对DMRG方法计算的有限尺寸系统的基态和第一激发态之间的能隙的数值数据进行了分析，结果表明，当无各向异性的基态具有霍尔丹特征时，各向异性引起伴随能隙消失的二阶相变，如均匀S=1链的情况2。S=1/2、S=1、S=3/2、S=1自旋按此顺序周期性排列的自旋-1/2-1/ 3/2-1链，与上述自旋-1/2-1/2-1-1 -1链的情况类似，我们确定了自旋-1/2-1/ 3 -1-1链在交换相互作用常数平面上的基态相图。我们发现了几种基态相，它们都具有二聚体特征。我们将我们的相图结果与Takano通过将自旋哈密顿量映射到非线性σ模型中近似得到的结果进行了比较，并讨论了这种近似方法的适用性。少

We have investigated the ground states of the following two kinds of regularly mixed quantum spin chains :1.Spin-1/2-1/2-1-1 chain in which two S=1/2 and two S=1 spins are arranged alternativelyWe have determined the ground-state phase diagram of the spin-1/2-1/2-1-1 chain on an exchange interaction constant plane where the exchange interaction between S=1 spins are antiferromagnetic, employing analytical methods based on the Lieb-Mattis theorem and the Wigner-Eckart theorem as well as numerical methods such as a method of exact diagonalization for finite-size systems and a density-matrix renormalization-group (DMRG) method. We have also calculated the two-spin correlation functions and the string order parameter in the ground states, and have presented a characterization of the phases concerning how the ground state in each phase is represented in the framework of the valence-bond-solid (VBS) picture. These results show that five phases among eleven phases appearing in the ground-stat … More e phase diagram are of dimer character, while the remaining six phases are of Haldane character.Furthermore, we have studied the effect of the uniaxial single-ion-type anisotropy for the S=1 spins on the ground state of the spin-1/2-1/2-1-1 chain. Analyzing, by applying the phenomenological renormalization-group (PRG) method, the numerical data for the energy gap between the ground and first-excited states of finite-size systems calculated by the DMRG method, we have shown that, when the ground state in the case of no anisotropy is of Haldane character, the anisotropy causes a second-order phase transition accompanying the disappearance of the energy gap, as in the case of the uniform S=1 chain.2.Spin-1/2-1-3/2-1 chain in which the S=1/2, S=1, S=3/2, and S=1 spins are arranged periodically in this orderIn a way similar to the case of the above spin-1/2-1/2-1-1 chain, we have determined the ground-state phase diagram of the Spin-1/2-1-3/2-1 chain on an exchange interaction constant plane. We have found a few kinds of ground-state phases, which are all of dimer character. We have compared our result for the phase diagram with Takano's result obtained approximately by mapping the spin Hamiltonian into the nonlinear σ model, and have discussed the applicability of this approximate method. Less