Abstract:
We investigate the mixed diamond chain composed of spins 1 and 1/2 when the exchange interaction is alternatingly distorted. Depending on the strengths of frustration and distortion, this system has various ground states. Each ground state consists of an array of spin clusters separated by singlet dimers by virtue of an infinite number of local conservation laws. We determine the ground state phase diagram by numerically analyzing each spin cluster. In particular for strong distortion, we find an infinite series of quantum phase transitions by the cluster expansion method and conformal field theory. This leads to the infinite series of steps in the behavior of the Curie constant and residual entropy.

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:
The mixed diamond chain is a frustrated Heisenberg chain composed of successive diamond-shaped units with two kinds of spins of magnitudes S and S/2 (S: integer). Ratio $lambda$ of two exchange parameters controls the strength of frustration. With varying $lambda$, the Haldane state and several spin cluster states appear as the ground state. A spin cluster state is a tensor product of exact local eigenstates of cluster spins. We prove that a spin cluster state is the ground state in a finite interval of $lambda$. For S=1, we numerically determine the total phase diagram consisting of five phases.

Abstract:
The ground states of two types of distorted mixed diamond chains with spins 1 and 1/2 are investigated using exact diagonalization, DMRG, and mapping onto low-energy effective models. In the undistorted case, the ground state consists of an array of independent spin-1 clusters separated by singlet dimers. The lattice distortion induces an effective interaction between cluster spins. When this effective interaction is antiferromagnetic, several Haldane phases appear with or without spontaneous translational symmetry breakdown (STSB). The transition between the Haldane phase without STSB and that with $(n+1)$-fold STSB ($n$ = 1, 2, and 3) belongs to the same universality class as the $(n+1)$-clock model. In contrast, when the effective interaction is ferromagnetic, the quantized and partial ferrimagnetic phases appear with or without STSB. An effective low-energy theory for the partial ferrimagnetic phase is presented.

Abstract:
The ground state and magnetization process of the mixed spin-(1,1/2) Ising diamond chain is exactly solved by employing the generalized decoration-iteration mapping transformation and the transfer-matrix method. The decoration-iteration transformation is first used in order to establish a rigorous mapping equivalence with the corresponding spin-1 Blume-Emery-Griffiths chain in a non-zero magnetic field, which is subsequently exactly treated within the framework of the transfer-matrix technique. It is shown that the ground-state phase diagram includes just four different ground states and the low-temperature magnetization curve may exhibit an intermediate plateau precisely at one half of the saturation magnetization. Our rigorous results disprove recent Monte Carlo simulations of Zihua Xin et al. [Z. Xin, S. Chen, C. Zhang, J. Magn. Magn. Mater. 324 (2012) 3704], which imply an existence of the other magnetization plateaus at 0.283 and 0.426 of the saturation magnetization.

Abstract:
The symmetric spin-1/2 Ising-Heisenberg diamond chain with different Land\'e g-factors of Ising and Heisenberg spins is exactly solved by combining the generalized decoration-iteration transformation and transfer-matrix method. The ground state of the system and magnetocaloric effect during the adiabatic (de)magnetization are particularly examined. It is evidenced that the considered mixed-spin diamond chain exhibits an enhanced magnetocaloric effect during the adiabatic (de)magnetization in the vicinity of field-induced phase transitions as well as in the zero-field limit if the frustrated phase constitutes the zero-field ground state, but the cooling efficiency depends on whether the system is macroscopically degenerate in these parameter regions or not.

Abstract:
We present results on the dynamics of the distorted diamond chain, S=1/2 dimers alternating with single spins 1/2 and exchange couplings $J_1$ and $J_3$ in between. The dynamics in the spin fluid (SF) and tetramer-dimer (TD) phases is investigated numerically by exact diagonalisation for up to 24 spins. Representative excitation spectra are presented, both for zero magnetic field and in the 1/3 plateau phase and the relevant parameters are determined across the phase diagram. The behavior across the SF-TD phase transition line is discussed for the specific heat and for excitation spectra. The relevance of the distorted diamond chain model for the material Cu$_3$(CO$_3$)$_2$(OH)$_2$ (azurite) is discussed with particular emphasis on inelastic neutron scattering experiments, a recent suggestion of one possibly ferromagnetic coupling constant is not confirmed.

Abstract:
The strongly correlated spin-electron system on a diamond chain containing localized Ising spins on its nodal lattice sites and mobile electrons on its interstitial sites is exactly solved in a magnetic field using the transfer-matrix method. We have investigated in detail all available ground states, the magnetization processes, the spin-spin correlation functions around an elementary plaquette, fermionic quantum concurrence and spin frustration. It is shown that the fermionic entanglement between mobile electrons hopping on interstitial sites and the kinetically-induced spin frustration are closely related yet independent phenomena. In the ground state, quantum entanglement only appears within a frustrated unsaturated paramagnetic phase, while thermal fluctuations can promote some degree of quantum entanglement above the non-frustrated ground states with saturated paramagnetic or classical ferrimagnetic spin arrangements.

Abstract:
An exactly solvable variant of mixed spin-(1/2,1) Ising-Heisenberg diamond chain is considered. Vertical spin-1 dimers are taken as quantum ones with Heisenberg bilinear and biquadratic interactions and with single-ion anisotropy, while all interactions between spin-1 and spin-1/2 residing on the intermediate sites are taken in the Ising form. The detailed analysis of the $T=0$ ground state phase diagram is presented. The phase diagrams have shown to be rather rich, demonstrating large variety of ground states: saturated one, three ferrimagnetic with magnetization equal to 3/5 and another four ferrimagnetic ground states with magnetization equal to 1/5. There are also two frustrated macroscopically degenerated ground states which could exist at zero magnetic filed. Solving the model exactly within classical transfer-matrix formalism we obtain an exact expressions for all thermodynamic function of the system. The thermodynamic properties of the model have been described exactly by exact calculation of partition function within the direct classical transfer-matrix formalism, the entries of transfer matrix, in their turn, contain the information about quantum states of vertical spin-1 XXZ dimer (eigenvalues of local hamiltonian for vertical link).