Abstract:
By the analytical coupled cluster method (CCM), we study both the ground state and lowest-lying excited-state properties of the alternating bond diamond chain. The numerical exact diagonalization (ED) method is also applied to the chain to verify the accuracy of CCM results. The ED results show that the ground-state phase diagram contains two exact spin cluster solid ground states, namely, the tetramer-dimer (TD) state and dimer state, and the ferrimagnetic long-range-ordered state. We prove that the two exact spin cluster solid ground states can both be formed by CCM. Moreover, the exact spin gap in the TD state can be obtained by CCM. In the ferrimagnetic region, we find that the CCM results for some physical quantities, such as the ground-state energy, the sublattice magnetizations, and the antiferromagnetic gap, are comparable to the results obtained by numerical methods. The critical line dividing the TD state from the ferrimagnetic state is also given by CCM and is in perfect agreement with that determined by the ED method.

Abstract:
Effects of single-site anisotropy on mixed diamond chains with spins 1 and 1/2 are investigated in the ground states and at finite temperatures. There are phases where the ground state is a spin cluster solid, i.e., an array of uncorrelated spin-1 clusters separated by singlet dimers. The ground state is nonmagnetic for the easy-plane anisotropy, while it is paramagnetic for the easy-axis anisotropy. Also, there are the N\'eel, Haldane, and large-$D$ phases, where the ground state is a single spin cluster of infinite size and the system is equivalent to the spin-1 Heisenberg chain with alternating anisotropy. The longitudinal and transverse susceptibilities and entropy are calculated at finite temperatures in the spin-cluster-solid phases. Their low-temperature behaviors are sensitive to anisotropy.

Abstract:
The ground-state phases of anisotropic mixed diamond chains with spins 1 and 1/2 are investigated. Both single-site and exchange anisotropies are considered. We find the phases consisting of an array of uncorrelated spin-1 clusters separated by singlet dimers. Except in the simplest case where the cluster consists of a single $S=1$ spin, this type of ground state breaks the translational symmetry spontaneously. Although the mechanism leading to this type of ground state is the same as that in the isotropic case, it is nonmagnetic or paramagnetic depending on the competition between two types of anisotropy. We also find the N\'eel, period-doubled N\'eel, Haldane, and large-$D$ phases, where the ground state is a single spin cluster of infinite size equivalent to the spin-1 Heisenberg chain with alternating anisotropies. The ground-state phase diagrams are determined for typical sets of parameters by numerical analysis. In various limiting cases, the ground-state phase diagrams are determined analytically. The low-temperature behaviors of magnetic susceptibility and entropy are investigated to distinguish each phase by observable quantities. The relationship of the present model with the anisotropic rung-alternating ladder with spin-1/2 is also discussed.

Abstract:
Susceptibility, ESR and magnetization measurements have been performed on si ngle crystals of an S=1 bond alternating chain compound: [Ni(333-tet)(\mu-NO _2)](ClO_4) (333-tet = N,N'-bis(3-aminopropyl)propane-1,3-diamine) and the c ompound doped with a small amount of Zn. We observed an anomalous angular de pendence in the Zn-doped sample. These behaviors are well explained by the m odel based on the VBS picture for the singlet-dimer phase. The picture impli es that the free spins of S=1 with a positive single-ion anisotropy are indu ced at the edges of the chains without forming the singlet-dimer.

Abstract:
We present results for the dynamic structure factor of the S=1/2 bond alternating Heisenberg chain over a large range of frequencies and temperatures. Data are obtained from a numerical evaluation of thermal averages based on the calculation of all eigenvalues and eigenfunctions for chains of up to 20 spins. Interpretation is guided by the exact temperature dependence in the noninteracting dimer limit which remains qualitatively valid up to an interdimer exchange $\lambda \approx 0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spin diffusion in its variation from low to high temperatures are discussed. The one-magnon peak acquires an asymmetric shape with increasing temperature. The two-magnon peak is dominated by the S=1 bound state which remains well defined up to temperatures of the order of J. The variation with temperature and wavevector of the integrated intensity for one and two magnon scattering and of the central peak are discussed.

Abstract:
We make a matrix-product variational approach to spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chains with anisotropy on their ferromagnetic bonds, especially under the open boundary condition. The rich phase diagram containing the Haldane, large-D, and two types of Neel phases is well reproduced with only two variational parameters. The on-bond anisotropy has a significant effect on the ferromagnetic coupling between neighboring spins and induces novel edge states peculiar to spin-1/2 chains.

Abstract:
We formulate statistical mechanics for the mixed diamond chain with spins of magnitudes 1 and 1/2. Owing to a series of conservation laws, any eigenstate of this system is decomposed into eigenstates of finite odd-length spin-1 chains. The ground state undergoes five quantum phase transitions with varying the parameter $\lambda$ controlling frustration. We obtain the values of the residual entropy and the Curie constant which characterize each phase and phase boundary at low temperatures. We further find various characteristic finite-temperature properties such as the nonmonotonic temperature dependence of the magnetic susceptibility, the multipeak structure in the $\lambda$-dependence of entropy, the plateau-like temperature dependence of entropy and the multipeak structure of specific heat.

Abstract:
Susceptibility and high field magnetization measurements have been performed on powder samples of an $S$=1 bond alternating chain compound [\{Ni(333-tet)($\mu$-N$_3$)\}$_n$](ClO$_4$)$_n$ (333-tet=tetraamine N,N'-bis(3-aminopropyl)-1,3-propanediamine). As the temperature is decreased, the susceptibility exhibits a round maximum at around 120 K and decreases gradually down to 10 K, and then falls down rapidly with a logarithmic curvature which is behavior of the susceptibility of a gapless or a nearly gapless antiferromagnetic chain. Magnetization up to 50 T at 1.4 K shows no or a very small gap in this compound. We have carried out numerical calculations for the $S$=1 antiferromagnetic bond alternating chain with various alternating ratios $\alpha$ and obtained a very good agreement between experiments and calculations for $\alpha$=0.6. We verify experimentally that the gapless point exists around $\alpha$=0.6.

Abstract:
The mixture of bond-alternating and uniform S=1/2 antiferromagnetic Heisenberg chains is investigated by the density matrix renormalization group method. The ground state magnetization curve is calculated and the exchange parameters are determined by fitting to the experimentally measured magnetization curve of \CuCl$_{2x}$Br$_{2(1-x)}$($\gamma$-pic)$_2$. The low field behavior of the magnetization curve and low temperature behavior of the magnetic susceptibility are found to be sensitive to whether the bond-alternation pattern (parity) is fixed all over the sample or randomly distributed. The both quantities are compatible with the numerical results for the random parity model.

Abstract:
The phase transitions between the XY, the dimer and the Haldane phases of the spin-1 bond-alternating XXZ chain are studied by the numerical diagonalization. We determine the phase diagram at $T=0$ and also identify the universality class with the level spectroscopy. We find that exactly on $\Delta=0$ there is a Berezinskii-Kosterlitz-Thouless transition line which separates the XY and the Haldane phase and there exists a multicritical point of the XY, the dimer and the Haldane phases. We discuss that the critical properties of this model is of the 2-D Ashkin-Teller type reflecting the hidden $Z_2\times Z_2$ symmetry.