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

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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