arXiv:cond-mat/9809291 · Physical review. B, Condensed matter

Magnetization plateau in the spin ladder with a four-spin exchange

Tôru Sakai, Yasumasa Hasegawa

Published Jul 1, 1999• 26 citations

Abstract

The magnetization process of the $S=1/2$ antiferromagnetic spin ladder with the four-spin cyclic exchange interaction 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 if the ratio of the four- and two-spin exchange coupling constants ${J}_{4}$ is larger than the critical value ${J}_{4c}=0.05\ifmmode\pm\else\textpm\fi{}0.04.$ The phase transition with respect to ${J}_{4}$ at ${J}_{4c}$ is revealed to be the Kosterlitz-Thouless type.

DOI: 10.1103/physrevb.60.48

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The field-induced gap due to four-spin exchange in a spin ladder

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Quantum phase transition by cyclic four-spin exchange interaction for S=1/2 two-leg spin ladder

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arXiv:cond-mat/9809291 · Physical review. B, Condensed matter

Magnetization plateau in the spin ladder with a four-spin exchange

Tôru Sakai, Yasumasa Hasegawa

Published Jul 1, 1999• 26 citations

arXiv HTML PDF

Abstract

The magnetization process of the

S=1/2

antiferromagnetic spin ladder with the four-spin cyclic exchange interaction 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 if the ratio of the four- and two-spin exchange coupling constants

{J}_{4}

is larger than the critical value

{J}_{4c}=0.05\ifmmode\pm\else\textpm\fi{}0.04.

The phase transition with respect to

{J}_{4}

{J}_{4c}

is revealed to be the Kosterlitz-Thouless type.

DOI: 10.1103/physrevb.60.48

Related papers

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.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/9912234Journal of the Physical Society of JapanJan 1, 200018 citations

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敦志中須, Keisuke Totsuka, Yasumasa Hasegawa +2 more

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Quantum phase transition by cyclic four-spin exchange interaction for S=1/2 two-leg spin ladder

Honda, Yasushi, Tsuyoshi Horiguchi

We investigate an $S=1/2$ two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by $J_4$ , by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by $J_{rung}$ and $J_{\rm leg}$ , respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet ( $S_{tot}^z=0$ ) and the triplet ( $S_{tot}^z=1$ ) states vanishes at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$ . This result is in contrast with the fact that the $S=1/2$ antiferromagnetic Heisenberg ladder, that is the case of $J_{rung} \neq J_{leg}, J_4=0$ , has a spin gap for all nonzero value of interchain interaction $J_{\rm rung}>0$ . We find a larger value of the correlation length for the spin-pair correlation function than a linear size $L$ of the system at $J_4/J_{\rm leg}=0.3$ and $J_{rung}=J_{leg}$ : the correlation length $ξ$ is about 204 times of the lattice constant for L=84 for these values of interactions. We also find that the string correlation function decays rather algebraically than exponentially at $J_4/J_{leg}=0.3$ and $J_{rung}=J_{leg}$ . These results suggest that there is a quantum phase transition at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$ . We estimate a phase boundary where the spin gap vanishes in a $J_4/J_{leg}-J_{rung}/J_{leg}$ plane and obtain a consistent result with that by a perturbation theory for $J_{\rm rung}/J_{leg}>1$ .We investigate an $S=1/2$ two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by $J_4$, by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by $J_{rung}$ and $J_{\rm leg}$, respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet ($S_{tot}^z=0$) and the triplet ($S_{tot}^z=1$) states vanishes at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$. This result is in contrast with the fact that the $S=1/2$ antiferromagnetic Heisenberg ladder, that is the case of $J_{rung} \neq J_{leg}, J_4=0$, has a spin gap for all nonzero value of interchain interaction $J_{\rm rung}>0$. We find a larger value of the correlation length for the spin-pair correlation function than a linear size $L$ of the system at $J_4/J_{\rm leg}=0.3$ and $J_{rung}=J_{leg}$: the correlation length $ξ$ is about 204 times of the lattice constant for L=84 for these values of interactions. We also find that the string correlation function decays rather algebraically than exponentially at $J_4/J_{leg}=0.3$ and $J_{rung}=J_{leg}$. These results suggest that there is a quantum phase transition at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$. We estimate a phase boundary where the spin gap vanishes in a $J_4/J_{leg}-J_{rung}/J_{leg}$ plane and obtain a consistent result with that by a perturbation theory for $J_{\rm rung}/J_{leg}>1$.

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We have studied the ground state phase diagram of a spin ladder with alternating rung exchange $J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]$ in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mapped onto an $XXZ$ Heisenberg chain in a uniform and staggered longitudinal magnetic fields, where the amplitude of the staggered field is $\sim δ$ . We have shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. The width of a plateau scales as $δ^ν$ , where $ν=4/5$ in the case of ladder with isotropic antiferromagnetic legs and $ν=2$ in the case of ladder with isotropic ferromagnetic legs. We have calculated four critical fields ( $H^{\pm}_{c1}$ and $H^{\pm}_{c2}$ ) corresponding to transitions between different magnetic phases of the system. We have shown that these transitions belong to the universality class of the commensurate-incommensurate transition.We have studied the ground state phase diagram of a spin ladder with alternating rung exchange $J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]$ in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mapped onto an $XXZ$ Heisenberg chain in a uniform and staggered longitudinal magnetic fields, where the amplitude of the staggered field is $\sim δ$. We have shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. The width of a plateau scales as $δ^ν$, where $ν=4/5$ in the case of ladder with isotropic antiferromagnetic legs and $ν=2$ in the case of ladder with isotropic ferromagnetic legs. We have calculated four critical fields ($H^{\pm}_{c1}$ and $H^{\pm}_{c2}$) corresponding to transitions between different magnetic phases of the system. We have shown that these transitions belong to the universality class of the commensurate-incommensurate transition.

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Translational Symmetry Broken Magnetization Plateau of the $S={{1}\over{2}}$ Anisotropic Spin Ladder with Ferromagnetic Rung InteractionTranslational Symmetry Broken Magnetization Plateau of the $S={{1}\over{2}}$ Anisotropic Spin Ladder with Ferromagnetic Rung Interaction

Tôru Sakai, Doi, Koki, Kiyomi Okamoto +5 more

The magnetization process of the $S=1/2$ anisotropic spin ladder with the ferromagnetic rung interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the translational symmetry broken magnetization plateau would appear at half the saturation magnetization, when the competing anisotropies are sufficiently large. The phase diagram with respect to the anisotropies and several magnetization curves are presented.The magnetization process of the $S=1/2$ anisotropic spin ladder with the ferromagnetic rung interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the translational symmetry broken magnetization plateau would appear at half the saturation magnetization, when the competing anisotropies are sufficiently large. The phase diagram with respect to the anisotropies and several magnetization curves are presented.

arXiv:2505.02367May 5, 20250 citations

The magnetization process of the

S=1/2

antiferromagnetic spin ladder with the four-spin cyclic exchange interaction at

T=0

{J}_{4}

is larger than the critical value

{J}_{4c}=0.05\ifmmode\pm\else\textpm\fi{}0.04.

The phase transition with respect to

{J}_{4}

{J}_{4c}

is revealed to be the Kosterlitz-Thouless type.

The effect of the four-spin cyclic exchange interaction at each plaquette in the

S=1/2

two-leg spin ladder is investigated at T=0, especially focusing on the field-induced gap. The strong rung coupling approximation suggests that it yields a plateau at half of the saturation moment (

m=1/2

) in the magnetization curve, which corresponds to a field-induced spin gap with a spontaneous breaking of the translational symmetry. A precise phase diagram at

m=1/2

is also presented based on the level spectroscopy analysis of the numerical data obtained by Lanczos method. The boundary between the gapless and plateau phases is confirmed to be of the Kosterlitz-Thouless (KT) universality class.

We investigate an

S=1/2

two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by

J_4

, by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by

J_{rung}

and

J_{\rm leg}

, respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet (

S_{tot}^z=0

) and the triplet (

S_{tot}^z=1

) states vanishes at

J_4/J_{leg} \simeq 0.3

for

J_{rung}=J_{leg}

. This result is in contrast with the fact that the

S=1/2

antiferromagnetic Heisenberg ladder, that is the case of

J_{rung} \neq J_{leg}, J_4=0

, has a spin gap for all nonzero value of interchain interaction

J_{\rm rung}>0

. We find a larger value of the correlation length for the spin-pair correlation function than a linear size

L

of the system at

J_4/J_{\rm leg}=0.3

and

J_{rung}=J_{leg}

: the correlation length

ξ

is about 204 times of the lattice constant for L=84 for these values of interactions. We also find that the string correlation function decays rather algebraically than exponentially at

J_4/J_{leg}=0.3

and

J_{rung}=J_{leg}

. These results suggest that there is a quantum phase transition at

J_4/J_{leg} \simeq 0.3

for

J_{rung}=J_{leg}

. We estimate a phase boundary where the spin gap vanishes in a

J_4/J_{leg}-J_{rung}/J_{leg}

plane and obtain a consistent result with that by a perturbation theory for

J_{\rm rung}/J_{leg}>1

We have studied the ground state phase diagram of a spin ladder with alternating rung exchange

J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]

in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mapped onto an

XXZ

Heisenberg chain in a uniform and staggered longitudinal magnetic fields, where the amplitude of the staggered field is

\sim δ

. We have shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. The width of a plateau scales as

δ^ν

, where

ν=4/5

in the case of ladder with isotropic antiferromagnetic legs and

ν=2

in the case of ladder with isotropic ferromagnetic legs. We have calculated four critical fields (

H^{\pm}_{c1}

and

H^{\pm}_{c2}

) corresponding to transitions between different magnetic phases of the system. We have shown that these transitions belong to the universality class of the commensurate-incommensurate transition.

The magnetization process of the

S

\frac{3}{2}

antiferromagnetic Heisenberg chain with single-ion anisotropy

D

T=0

is investigated by the exact diagonalization of finite clusters and finite-size scaling analyses. It is found that a magnetization plateau appears at

m=

\frac{1}{2}

for $D>{D}_{c}=0.93\ifmmode\pm\else\textpm\fi{}0.01$. The phase transition with respect to

D

{D}_{c}

is revealed to be of the Kosterlitz-Thouless type. The magnetization curve of the infinite system is also presented for some values of

D

Translational Symmetry Broken Magnetization Plateau of the

S={{1}\over{2}}

Anisotropic Spin Ladder with Ferromagnetic Rung Interaction

The magnetization process of the

S=1/2

anisotropic spin ladder with the ferromagnetic rung interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the translational symmetry broken magnetization plateau would appear at half the saturation magnetization, when the competing anisotropies are sufficiently large. The phase diagram with respect to the anisotropies and several magnetization curves are presented.