arXiv:cond-mat/0211458 · Journal of the Physical Society of Japan

Magnetic Phase Diagram of theS=1/2 Antiferromagnetic Zigzag Spin Chain in the Strongly Frustrated Region: Cusp and Plateau

Kouichi Okunishi, Takashi Tonegawa

Published Mar 15, 2003• 96 citations

Abstract

We determine the magnetic phase diagram of the antiferromagnetic(AF) zigzag spin chain in the strongly frustrated region, using the density matrix renormalization group method. We find the magnetization plateau at 1/3 of the full moment accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve. We also discuss the formation mechanisms of the plateau and cusps briefly.

DOI: 10.1143/jpsj.72.479

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arXiv:cond-mat/0211458 · Journal of the Physical Society of Japan

Magnetic Phase Diagram of theS=1/2 Antiferromagnetic Zigzag Spin Chain in the Strongly Frustrated Region: Cusp and Plateau

Kouichi Okunishi, Takashi Tonegawa

Published Mar 15, 2003• 96 citations

arXiv HTML PDF

Abstract

DOI: 10.1143/jpsj.72.479

Related papers

FractionalSzExcitation and Its Boundstate for theS=1/2 Antiferromagnetic Zigzag Spin Chain in a Magnetic Field

Kouichi Okunishi, Takashi Tonegawa

We demonstrate that domain-wall type excitations carrying the fractional magnetization $S^z=\pm1/3$ and their bound state describe the low-energy physics around the 1/3 plateau of the antiferromagnetic zigzag spin chain in the strongly frustrated region. In particular we discuss the relevance of such domain-wall excitations to the characteristic properties of the magnetization curves: the 1/3 plateau accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve.We demonstrate that domain-wall type excitations carrying the fractional magnetization $S^z=\pm1/3$ and their bound state describe the low-energy physics around the 1/3 plateau of the antiferromagnetic zigzag spin chain in the strongly frustrated region. In particular we discuss the relevance of such domain-wall excitations to the characteristic properties of the magnetization curves: the 1/3 plateau accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve.

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Ferrimagnetic states inS= 1/2 frustrated Heisenberg chains with period 3 exchange modulation

K Hida

The ground state properties of the S = 1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and density matrix renormalization group (DMRG) method. It is known that this model has a magnetization plateau at one third of the saturation magnetization M s . On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and the others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if the frustration is strong. This state further continues to the above-mentioned 1/3 plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than M s /3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.The ground state properties of the S = 1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and density matrix renormalization group (DMRG) method. It is known that this model has a magnetization plateau at one third of the saturation magnetization M s . On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and the others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if the frustration is strong. This state further continues to the above-mentioned 1/3 plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than M s /3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.

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Universal emergence of the one-third plateau in the magnetization process of frustrated quantum spin chains

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We present a numerical study of the magnetization process of frustrated quantum spin- $S$ chains with $S=1,3∕2,2$ as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin- $S$ chains with $S>1∕2$ . Similar to the case of $S=1∕2$ , this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this plateau exists both in the cases of an isotropic exchange and in the easy-axis regime for spin- $S=1$ , $3∕2$ , and 2, but is absent in classical frustrated spin chains with isotropic interactions. We discuss the magnetic phase diagram of frustrated spin-1 and spin- $3∕2$ chains as well as other emergent features of the magnetization process such as kink singularities, jumps, and even-odd effects. A quantitative comparison of the one-third plateau in the easy-axis regime between spin-1 and spin- $3∕2$ chains on the one hand and the classical frustrated chain on the other hand indicates that the critical frustration and the phase boundaries of this state rapidly approach the classical result as the spin $S$ increases.We present a numerical study of the magnetization process of frustrated quantum spin-$S$ chains with $S=1,3∕2,2$ as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin-$S$ chains with $S>1∕2$. Similar to the case of $S=1∕2$, this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this plateau exists both in the cases of an isotropic exchange and in the easy-axis regime for spin-$S=1$, $3∕2$, and 2, but is absent in classical frustrated spin chains with isotropic interactions. We discuss the magnetic phase diagram of frustrated spin-1 and spin-$3∕2$ chains as well as other emergent features of the magnetization process such as kink singularities, jumps, and even-odd effects. A quantitative comparison of the one-third plateau in the easy-axis regime between spin-1 and spin-$3∕2$ chains on the one hand and the classical frustrated chain on the other hand indicates that the critical frustration and the phase boundaries of this state rapidly approach the classical result as the spin $S$ increases.

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Translational symmetry broken magnetization plateau of the S=1 antiferromagnetic Heisenberg chain with competing anisotropies

Tôru Sakai, Kiyomi Okamoto, Kouichi Okunishi +4 more

We investigate the $S=1$ antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using numerical exact diagonalization of finite-size clusters, level spectroscopy analysis, and the density matrix renormalization group (DMRG). We find that a translational symmetry broken magnetization plateau possibly appears at the half of the saturation magnetization, when the anisotropies compete with each other. The level spectroscopy analysis gives the phase diagram at half the saturation magnetization. The DMRG calculation presents the magnetization curves for some typical parameters and clarifies the spin structure in the plateau phase.We investigate the $S=1$ antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using numerical exact diagonalization of finite-size clusters, level spectroscopy analysis, and the density matrix renormalization group (DMRG). We find that a translational symmetry broken magnetization plateau possibly appears at the half of the saturation magnetization, when the anisotropies compete with each other. The level spectroscopy analysis gives the phase diagram at half the saturation magnetization. The DMRG calculation presents the magnetization curves for some typical parameters and clarifies the spin structure in the plateau phase.

arXiv:2311.07123Physical review. B./Physical review. BNov 22, 20235 citations

We demonstrate that domain-wall type excitations carrying the fractional magnetization

S^z=\pm1/3

and their bound state describe the low-energy physics around the 1/3 plateau of the antiferromagnetic zigzag spin chain in the strongly frustrated region. In particular we discuss the relevance of such domain-wall excitations to the characteristic properties of the magnetization curves: the 1/3 plateau accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve.

We present a numerical study of the magnetization process of frustrated quantum spin-

S

chains with

S=1,3∕2,2

as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin-

S

chains with

S>1∕2

. Similar to the case of

S=1∕2

, this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this plateau exists both in the cases of an isotropic exchange and in the easy-axis regime for spin-

S=1

3∕2

, and 2, but is absent in classical frustrated spin chains with isotropic interactions. We discuss the magnetic phase diagram of frustrated spin-1 and spin-

3∕2

chains as well as other emergent features of the magnetization process such as kink singularities, jumps, and even-odd effects. A quantitative comparison of the one-third plateau in the easy-axis regime between spin-1 and spin-

3∕2

chains on the one hand and the classical frustrated chain on the other hand indicates that the critical frustration and the phase boundaries of this state rapidly approach the classical result as the spin

S

increases.

We investigate the

S=1

antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using numerical exact diagonalization of finite-size clusters, level spectroscopy analysis, and the density matrix renormalization group (DMRG). We find that a translational symmetry broken magnetization plateau possibly appears at the half of the saturation magnetization, when the anisotropies compete with each other. The level spectroscopy analysis gives the phase diagram at half the saturation magnetization. The DMRG calculation presents the magnetization curves for some typical parameters and clarifies the spin structure in the plateau phase.