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arXiv:1408.3890 · Journal of the Physical Society of Japan

Ground-State Phases of Anisotropic Mixed Diamond Chains with Spins 1 and 1/2

Kazuo Hida

Published Oct 28, 2014• 6 citations
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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 Néel, period-doubled Néel, 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.

DOI
10.7566/jpsj.83.114711

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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.
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 Néel, Haldane, and large-DDD 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.
Ground states and finite temperature properties of mixed diamond chains with spins 1 and1/2 which has the single-site anisotropy on spin-1 sites are investigated. There are phaseswhere the ground state is a spin cluster solid, i. e. an array of uncorrelated spin-1 clustersseparated 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, andlarge-D phases, where the ground state is a single spin cluster of infinite size and the systemis equivalent to the spin-1 Heisenberg chain with alternating anisotropy. The longitudinal andtransverse susceptibilities and entropy are calculated at finite temperatures in the spin-cluster-solid phases. Their low temperature behaviors are sensitive to the anisotropy.KEYWORDS: mixed diamond chain, anisotropy, frustration, spin cluster solid, N´eel phase, Haldane phase,large-Dphase
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.
Ground-State Phase Diagram of (1/2,1/2,1)(1/2,1/2,1)(1/2,1/2,1) Mixed Diamond Chains with Single-Site Anisotropy
The ground-state phases of mixed diamond chains with (S,τ(1),τ(2))=(1/2,1/2,1)S, τ^{(1)}, τ^{(2)})=(1/2,1/2,1)S,τ(1),τ(2))=(1/2,1/2,1), where SSS is the magnitude of vertex spins, and τ(1)τ^{(1)}τ(1) and τ(2)τ^{(2)}τ(2) are those of apical spins, are investigated with the single-site anisotropy DDD on the τ(2)τ^{(2)}τ(2)-site. The two apical spins in each unit cell are coupled by an exchange coupling λλλ. The vertex spins are coupled with the top and bottom apical spins by exchange couplings 1+δ1+δ1+δ and 1−δ1-δ1−δ, respectively. The ground-state phase diagram is determined using the numerical exact diagonalization and DMRG method in addition to the analytical approximations in various limiting cases. The phase diagram consists of a Néel ordered phase, a nonmagnetic Tomonaga-Luttinger liquid phase, and quantized and partial ferrimagnetic phases. A region with anisotropy inversion is found where the Ising-like Néel phase is realized for the easy-plane anisotropy D>0D >0D>0 and the XY-like Tomonaga-Luttinger liquid phase is realized for the easy-axis anisotropy D<0D <0D<0 on the S=1S=1S=1 sites.
Ground-State Phase Diagram of (1/2,1/2,1)(1/2,1/2,1)(1/2,1/2,1) Mixed Diamond Chains
The ground-state phases of mixed diamond chains with (S,τ(1),τ(2))=(1/2,1/2,1)S, τ^{(1)}, τ^{(2)})=(1/2,1/2,1)S,τ(1),τ(2))=(1/2,1/2,1), where SSS is the magnitude of vertex spins, and τ(1)τ^{(1)}τ(1) and τ(2)τ^{(2)}τ(2) are those of apical spins, are investigated. The two apical spins in each unit cell are coupled by an exchange coupling λλλ. The vertex spins are coupled with the top and bottom apical spins by exchange couplings 1+δ1+δ1+δ and 1−δ1-δ1−δ, respectively. Although this model has an infinite number of local conservation laws for δ=0δ=0δ=0, they are lost for finite δδδ. The ground-state phase diagram is determined using the numerical exact diagonalization and DMRG method in addition to the analytical approximations in various limiting cases. The phase diagram consists of a nonmagnetic phase and several kinds of ferrimagnetic phases. We find two different ferrimagnetic phases without spontaneous translational symmetry breakdown. It is also found that the quantized ferrimagnetic phases with large spatial periodicities present for δ=0δ=0δ=0 are easily destroyed by small δδδ and replaced by a partial ferrimagnetic phase. The nonmagnetic phase is considered to be a gapless Tomonaga-Luttinger liquid phase based on the recently extended Lieb-Schultz-Mattis theorem to the site-reflection invariant spin chains and numerical diagonalization results.
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.