arXiv:0811.1320 · Physical Review B

Exact spin-cluster ground states in a mixed diamond chain

Ken'ichi Takano, Hidenori Suzuki, Kazuo Hida

Published Sep 11, 2009• 18 citations

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 $\ensuremath{\lambda}$ 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 $S=1$, we numerically determine the total phase diagram consisting of five phases.

DOI: 10.1103/physrevb.80.104410

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arXiv:0811.1320 · Physical Review B

Exact spin-cluster ground states in a mixed diamond chain

Ken'ichi Takano, Hidenori Suzuki, Kazuo Hida

Published Sep 11, 2009• 18 citations

arXiv HTML PDF

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

\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=1

, we numerically determine the total phase diagram consisting of five phases.

DOI: 10.1103/physrevb.80.104410

Related papers

Ground states with cluster structures in a frustrated Heisenberg chain

K Takano, K Kubo, H Sakamoto

We examine the ground state of a Heisenberg model with arbitrary spin S on a one-dimensional lattice composed of diamond-shaped units. A unit includes two types of antiferromagnetic exchange interaction which frustrate each other. The system undergoes phase changes when the ratio between the exchange parameters varies. In some phases, strong frustration leads to larger local structures or clusters of spins than a dimer. We prove for arbitrary S that there exists a phase with four-spin cluster states, which was previously found numerically for a special value of in the S = 1/2 case. For S = 1/2 we show that there are three ground-state phases, and determine their boundaries.We examine the ground state of a Heisenberg model with arbitrary spin S on a one-dimensional lattice composed of diamond-shaped units. A unit includes two types of antiferromagnetic exchange interaction which frustrate each other. The system undergoes phase changes when the ratio between the exchange parameters varies. In some phases, strong frustration leads to larger local structures or clusters of spins than a dimer. We prove for arbitrary S that there exists a phase with four-spin cluster states, which was previously found numerically for a special value of in the S = 1/2 case. For S = 1/2 we show that there are three ground-state phases, and determine their boundaries.

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Ground-State Phase Diagram of $(1/2,1/2,1)$ Mixed Diamond ChainsGround-State Phase Diagram of $(1/2,1/2,1)$ Mixed Diamond Chains

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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-DphaseGround 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

Jun 20, 20110 citations

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

\ensuremath{\lambda}

of two exchange parameters controls the strength of frustration. With varying

\ensuremath{\lambda}

\ensuremath{\lambda}

. For

S=1

, we numerically determine the total phase diagram consisting of five phases.

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.

λ

, 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].

Ground-State Phase Diagram of

(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)

, where

S

is the magnitude of vertex spins, and

τ^{(1)}

and

τ^{(2)}

are those of apical spins, are investigated. The two apical spins in each unit cell are coupled by an exchange coupling

λ

. The vertex spins are coupled with the top and bottom apical spins by exchange couplings

1+δ

and

1-δ

, respectively. Although this model has an infinite number of local conservation laws for

δ=0

, they are lost for finite

δ

. 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=0

are easily destroyed by small

δ

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.