Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Phase Transitions

The magnetic field effects on the frustrated antiferromagnetic spin chain

M. Shahri Naseri, R. Kamran, S. Mahdavifar

Published Nov 30, 2016• 1 citation
Publisher

Abstract

We presented a numerical study of the magnetization process of frustrated spin-1/2 chain. Using the exact diagonalization technique, we provided the evidence that a plateau at one-third of the saturation magnetization exists in the magnetization curve of frustrated antiferromagnetic spin-1/2 chain.
DOI
10.1080/01411594.2016.1260716

Related papers

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

Fabian Heidrich‐Meisner, I. A. Sergienko, Adrian E. Feiguin +1 more

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.

arXiv:cond-mat/0609555•Physical Review B•Feb 12, 2007•45 citations

Magnetization Plateau in the Frustrated Spin Ladder

Nobuhisa Okazaki, Junji Miyoshi, Tôru Sakai

The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.

arXiv:cond-mat/9912234•Journal of the Physical Society of Japan•Jan 1, 2000•18 citations

Magnetization plateau of the S=2 antiferromagnetic Heisenberg chain with anisotropies

Tôru Sakai, Kiyomi Okamoto, Takashi Tonegawa

We investigate the $S=2$ antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetization curves are also presented. In addition, the biquadratic interaction is revealed to enhance the plateau induced by the Haldane mechanism.

arXiv:1907.11931•Physical review. B./Physical review. B•Aug 6, 2019•8 citations

Half magnetization plateau of a frustratedS= 1 antiferromagnetic chain

Takashi Tonegawa, Hiroki Nakano, Tôru Sakai +3 more

We numerically investigate the magnetization process of a frustrated S =1 chain with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) exchange interactions, which compete with each other, and also with uniaxial single-ion-type anisotropy energies. Special attention is paid to the half magnetization plateau which appears at the half of the saturation magnetization in the ground-state magnetization curve. We determine the parameter region where this plateau appears by employing the level spectroscopy method, and find that the plateau appears even in the absence of the single-ion-type anisotropy, if the ratio of the nnn to the nn interaction constant is in a specified region.

Journal of Physics Conference Series•Jan 1, 2010•0 citations

Quantum magnetization plateaux of an anisotropic ferrimagnetic spin chain

Tôru Sakai, Kiyomi Okamoto

The magnetization curve of the $(S,s)=(1,1/2)$ ferrimagnetic alternating spin chain with single-ion anisotropy D is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a plateau at (1/3) of the saturation moment, which corresponds to the spontaneous magnetization for $D=0.$ Varying D in the 1/3-magnetized ground state under the external field along the axis of D, a quantum phase transition is revealed to occur at the critical value $D/J=1.114\ifmmode\pm\else\textpm\fi{}0.001$ where the plateau vanishes. Except for the critical point, the plateau is always opening, but the mechanism is different between $D<{D}_{c}$ and $D>{D}_{c}.$ The change of mechanisms is an evidence to clarify that the plateau originates from the quantization of magnetization.

arXiv:cond-mat/0204375•Physical review. B, Condensed matter•May 16, 2002•60 citations

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

Kouichi Okunishi, Takashi Tonegawa

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.

arXiv:cond-mat/0211458•Journal of the Physical Society of Japan•Mar 15, 2003•96 citations
We present a numerical study of the magnetization process of frustrated quantum spin-SSS chains with S=1,3∕2,2S=1,3∕2,2S=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-SSS chains with S>1∕2S>1∕2S>1∕2. Similar to the case of S=1∕2S=1∕2S=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=1S=1S=1, 3∕23∕23∕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∕23∕23∕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∕23∕23∕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 SSS increases.
The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.
We investigate the S=2S=2S=2 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetization curves are also presented. In addition, the biquadratic interaction is revealed to enhance the plateau induced by the Haldane mechanism.
We numerically investigate the magnetization process of a frustrated S =1 chain with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) exchange interactions, which compete with each other, and also with uniaxial single-ion-type anisotropy energies. Special attention is paid to the half magnetization plateau which appears at the half of the saturation magnetization in the ground-state magnetization curve. We determine the parameter region where this plateau appears by employing the level spectroscopy method, and find that the plateau appears even in the absence of the single-ion-type anisotropy, if the ratio of the nnn to the nn interaction constant is in a specified region.
The magnetization curve of the (S,s)=(1,1/2)(S,s)=(1,1/2)(S,s)=(1,1/2) ferrimagnetic alternating spin chain with single-ion anisotropy D is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a plateau at (1/3) of the saturation moment, which corresponds to the spontaneous magnetization for D=0.D=0.D=0. Varying D in the 1/3-magnetized ground state under the external field along the axis of D, a quantum phase transition is revealed to occur at the critical value $D/J=1.114\ifmmode\pm\else\textpm\fi{}0.001$ where the plateau vanishes. Except for the critical point, the plateau is always opening, but the mechanism is different between D<DcD<{D}_{c}D<Dc​ and D>Dc.D>{D}_{c}.D>Dc​. The change of mechanisms is an evidence to clarify that the plateau originates from the quantization of magnetization.