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arXiv:0911.3838 · Journal of the Physical Society of Japan

Quantum Phase Transitions in Alternating-Bond Mixed Diamond Chains with Spins 1 and 1/2

Kazuo Hida, Ken'ichi Takano, Hidenori Suzuki

Published Mar 25, 2010• 14 citations
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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.

DOI
10.1143/jpsj.79.044702

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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.
The ground-state phases of alternating-bond spin-1 diamond chains are investigated. Each ground state consists of an array of spin clusters separated by singlet dimers owing to an infinite number of local conservation laws. If no singlet dimers are present, the ground state is equivalent to that of a spin chain with infinite length.For strong frustration, we find a series of quantum phase transitions as in the case of alternating-bond mixed diamond chains with spins 1 and 1/2. For intermediate frustration, we find the nonmagnetic Haldane or dimer phases according to whether the bond alternation is weak or strong. For weak frustration and weak bond alternation, we find the ferrimagnetic states with spontaneous magnetizations m=1/6m=1/6m=1/6 and 1/3 per site. The ferrimagnetic state with m=1/6m=1/6m=1/6 is accompanied by a spontaneous translational symmetry breakdown. This phase vanishes for strong bond alternation.
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=1S=1S=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 Néel, period-doubled Néel, Haldane, and large-DDD 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.
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 λλλ 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 λλλ-dependence of entropy, the plateau-like temperature dependence of entropy and the multipeak structure of specific heat.
The mixed diamond chain is a frustrated Heisenberg chain composed of successive diamond-shaped units with two kinds of spins of magnitudes SSS and S/2S/2S/2 (SSS: integer). Ratio $\ensuremath{\lambda}$ of two exchange parameters controls the strength of frustration. With varying $\ensuremath{\lambda}$, 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 $\ensuremath{\lambda}$. For S=1S=1S=1, we numerically determine the total phase diagram consisting of five phases.
We investigate the ground-state phase diagram of a spin-1 diamond chain. Owing to a series of conservation laws, any eigenstate of this system can be expressed using the eigenstates of finite odd-length chains or infinite chains with spins 1 and 2. The ground state undergoes quantum phase transitions with varying λλλ, a parameter that controls frustration. Exact upper and lower bounds for the phase boundaries between these phases are obtained. The phase boundaries are determined numerically in the region not explored in the previous work [Takano et al. J. Phys.: Condens. Matter 8 (1996) 6405].