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

arXiv:cond-mat/9809138 · Journal of Physics A Mathematical and General

Magnetization plateau and quantum phase transition of theS= ½ trimerizedXXZspin chain

Kiyomi Okamoto, Atsuhiro Kitazawa

Published Jan 1, 1999• 32 citations
arXivHTMLPDF

Abstract

We study the plateau of the magnetization curve at M = M s /3 ( M s is the saturation magnetization) of the S = ½ trimerized XXZ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the - t plane, where denotes the XXZ anisotropy and t the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.

DOI
10.1088/0305-4470/32/25/304

Related papers

Breakdown of the magnetization plateau of theS= 1/2 ferromagnetic-ferromagnetic-antiferromagnetic trimerized spin chain with anisotropy

Atsuhiro Kitazawa, Kiyomi Okamoto

We study the breakdown of the magnetization plateau at the magnetization M = M S /3 ( M S is the saturation magnetization) of the S = 1/2 anisotropic spin chain with ferromagnetic-ferromagnetic-antiferromagnetic interactions. We consider the model with the isotropic ferromagnetic (trimer) coupling J F , and anisotropic antiferromagnetic coupling ( J x = J y = J AF and J z = J AF ). For the limit of large J F / J AF , the model is equivalent to the S = 3/2 XXZ chain with the exchange anisotropy . There is a phase transition between the plateau (small- ) and the no-plateau (large- ) regions. This phase transition is of the Berezinskii-Kosterlitz-Thouless type, and we determine the phase boundary from the numerical diagonalization data. For = 1, in particular, the phase transition between the plateau and the no-plateau regions occurs at the point c = 15.4.

arXiv:cond-mat/9908027•Journal of Physics Condensed Matter•Nov 17, 1999•22 citations

Magnetization Plateau in the Frustrated Alternating Spin Chain

Tetsuji Kuramoto

We study the magnetization plateau at m =1/2 in the S =1/2 and S =1 alternating spin Heisenberg chain with two next-nearest-neighbor (NNN) interactions J a between neighboring S =1/2 spins and J b between neighboring S =1 spins, using the numerical diagonalization and the density-matrix renormalization group (DMRG) method. We present the m =1/2 plateau phase diagram in the J a – J b plane obtained by the level crossing method useful for the Berezinskii–Kosterlitz–Thouless (BKT) transition. In this phase diagram, we find that there are two plateau phases distinguished by a parity of the alternating spin chain.

Journal of the Physical Society of Japan•Sep 15, 2004•1 citation

Magnetization plateaus and phase diagram in polymerized S=1/2 XXZ chains

Wei Chen, Kazuo Hida, B. C. Sanctuary

The magnetization plateaus of polymerized $S=\frac{1}{2}$ $\mathrm{XXZ}$ chains are studied for general values of p. Two plateau-non-plateau critical lines and one plateau-plateau critical line are found for each value of p. The universality class of the plateau-non-plateau transition belongs to the Brezinskii-Kosterlitz-Thouless type and that of the plateau-plateau transition, to the Gaussian type. The critical points are determined by level spectroscopic analysis of the numerical diagonalization results for $4<~p<~8.$ The multicritical points are calculated using the integral equations based on the Bethe ansatz solution of the $\mathrm{XXZ}$ model. The behavior of multicritical points are analyzed in detail for large p. It is found that the plateau region is enhanced with the increase in periodicity p although the nonplateau region persists as far as p is finite.

arXiv:cond-mat/0009481•Physical review. B, Condensed matter•Mar 14, 2001•11 citations

Magnetization Process of (S= 3/2,S= 1) Anisotropic Ferrimagnetic Spin Chain

Shun Tonooka, Hiroki Nakano, Koichi Kusakabe +1 more

Magnetization process of ( S = 3/2, S = 1) ferrimagnetic spin chain with single-ion anisotropy D is investigated by numerical diagonalization. The magnetization process has a plateau at 1/5 of the saturation moment in the small D region. We find a quantum phase transition that the plateau once vanishes at a critical D and revives in the large D region. The critical value D c is estimated to be 0.9. In order to clarify the mechanism of this transition, we propose new trial states: a pentamer state in the small D phase and a trimer state in the large D phase. We find that representative ground state is changed from the pentamer state to the trimer one, while D increases across D c. This result suggests that the mechanism of the quantum phase transition is understood as the change of the representative ground state.

Progress of Theoretical Physics Supplement•Jan 1, 2005•3 citations

Magnetization plateau of the distorted diamond spin chain with anisotropic ferromagnetic interaction

Tôru Sakai, Kiyomi Okamoto, Hiroki Nakano +1 more

The S = 1/2 distorted diamond spin chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization and the level spectroscopy analysis. It is known that the system exhibits a plateau of the magnetization curve at the 1/3 of the saturation. The present study indicates that as the anisotropy is varied the quantum phase transition occurs between two different mechanisms of the 1/3 magnetization plateau. The phase diagram with respect to the anisotropy and the ferromagnetic coupling is also presented.

arXiv:2205.07027•AIP Advances•Mar 1, 2022•3 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
We study the plateau of the magnetization curve at M = M s /3 ( M s is the saturation magnetization) of the S = ½ trimerized XXZ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the - t plane, where denotes the XXZ anisotropy and t the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.
We study the breakdown of the magnetization plateau at the magnetization M = M S /3 ( M S is the saturation magnetization) of the S = 1/2 anisotropic spin chain with ferromagnetic-ferromagnetic-antiferromagnetic interactions. We consider the model with the isotropic ferromagnetic (trimer) coupling J F , and anisotropic antiferromagnetic coupling ( J x = J y = J AF and J z = J AF ). For the limit of large J F / J AF , the model is equivalent to the S = 3/2 XXZ chain with the exchange anisotropy . There is a phase transition between the plateau (small- ) and the no-plateau (large- ) regions. This phase transition is of the Berezinskii-Kosterlitz-Thouless type, and we determine the phase boundary from the numerical diagonalization data. For = 1, in particular, the phase transition between the plateau and the no-plateau regions occurs at the point c = 15.4.
We study the magnetization plateau at m =1/2 in the S =1/2 and S =1 alternating spin Heisenberg chain with two next-nearest-neighbor (NNN) interactions J a between neighboring S =1/2 spins and J b between neighboring S =1 spins, using the numerical diagonalization and the density-matrix renormalization group (DMRG) method. We present the m =1/2 plateau phase diagram in the J a – J b plane obtained by the level crossing method useful for the Berezinskii–Kosterlitz–Thouless (BKT) transition. In this phase diagram, we find that there are two plateau phases distinguished by a parity of the alternating spin chain.
The magnetization plateaus of polymerized S=12S=\frac{1}{2}S=21​ XXZ\mathrm{XXZ}XXZ chains are studied for general values of p. Two plateau-non-plateau critical lines and one plateau-plateau critical line are found for each value of p. The universality class of the plateau-non-plateau transition belongs to the Brezinskii-Kosterlitz-Thouless type and that of the plateau-plateau transition, to the Gaussian type. The critical points are determined by level spectroscopic analysis of the numerical diagonalization results for 4< p< 8.4<~p<~8.4< p< 8. The multicritical points are calculated using the integral equations based on the Bethe ansatz solution of the XXZ\mathrm{XXZ}XXZ model. The behavior of multicritical points are analyzed in detail for large p. It is found that the plateau region is enhanced with the increase in periodicity p although the nonplateau region persists as far as p is finite.
Magnetization process of ( S = 3/2, S = 1) ferrimagnetic spin chain with single-ion anisotropy D is investigated by numerical diagonalization. The magnetization process has a plateau at 1/5 of the saturation moment in the small D region. We find a quantum phase transition that the plateau once vanishes at a critical D and revives in the large D region. The critical value D c is estimated to be 0.9. In order to clarify the mechanism of this transition, we propose new trial states: a pentamer state in the small D phase and a trimer state in the large D phase. We find that representative ground state is changed from the pentamer state to the trimer one, while D increases across D c. This result suggests that the mechanism of the quantum phase transition is understood as the change of the representative ground state.
The S = 1/2 distorted diamond spin chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization and the level spectroscopy analysis. It is known that the system exhibits a plateau of the magnetization curve at the 1/3 of the saturation. The present study indicates that as the anisotropy is varied the quantum phase transition occurs between two different mechanisms of the 1/3 magnetization plateau. The phase diagram with respect to the anisotropy and the ferromagnetic coupling is also presented.
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.