arXiv:1611.10050 · Journal of the Physical Society of Japan

Ground-State Phase Diagram ofS= 1 Diamond Chains

Kazuo Hida, Ken'ichi Takano

Published Mar 1, 2017• 11 citations

Abstract

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 $λ$, 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].

DOI: 10.7566/jpsj.86.033707

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arXiv:1611.10050 · Journal of the Physical Society of Japan

Ground-State Phase Diagram ofS= 1 Diamond Chains

Kazuo Hida, Ken'ichi Takano

Published Mar 1, 2017• 11 citations

arXiv HTML PDF

Abstract

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].

DOI: 10.7566/jpsj.86.033707

Related papers

Finite Temperature Properties of Mixed Diamond Chain with Spins 1 and 1/2

Kazuo Hida, Ken'ichi Takano, Hidenori Suzuki

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 $λ$ 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 $λ$ -dependence of entropy, the plateau-like temperature dependence of entropy and the multipeak structure of specific heat.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 $λ$ 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 $λ$-dependence of entropy, the plateau-like temperature dependence of entropy and the multipeak structure of specific heat.

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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.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.

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λ

λ

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

λ

-dependence of entropy, the plateau-like temperature dependence of entropy and the multipeak structure of specific heat.

m=1/6

and 1/3 per site. The ferrimagnetic state with

m=1/6

is accompanied by a spontaneous translational symmetry breakdown. This phase vanishes for strong bond alternation.

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.

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.