Physical review. B, Condensed matter

Magnetization plateau in the S= 12 Heinsenberg spin chain with next-nearest-neighbor and alternating nearest-neighbor interactions

Keisuke Totsuka

Published Feb 1, 1998• 245 citations

Abstract

The magnetization process of the $S=1/2$ Heisenberg chain with next-nearest-neighbor (NNN) and alternating nearest-neighbor interactions is investigated using the bosonization technique. The existence of the NNN interaction is shown to stabilize a ``diluted'' dimer order at magnetization ${m}^{z}=1/4,$ leading to a plateau, where two degenerate ground states appear. Effective Hamiltonians describing the low-energy physics in the vicinity of the ${m}^{z}=1/4$ plateau are also presented. The analogy to metal-insulator transitions is discussed briefly.

DOI: 10.1103/physrevb.57.3454

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Physical review. B, Condensed matter

Magnetization plateau in the S= 12 Heinsenberg spin chain with next-nearest-neighbor and alternating nearest-neighbor interactions

Keisuke Totsuka

Published Feb 1, 1998• 245 citations

Publisher

Abstract

The magnetization process of the

S=1/2

Heisenberg chain with next-nearest-neighbor (NNN) and alternating nearest-neighbor interactions is investigated using the bosonization technique. The existence of the NNN interaction is shown to stabilize a ``diluted'' dimer order at magnetization

{m}^{z}=1/4,

leading to a plateau, where two degenerate ground states appear. Effective Hamiltonians describing the low-energy physics in the vicinity of the

{m}^{z}=1/4

plateau are also presented. The analogy to metal-insulator transitions is discussed briefly.

DOI: 10.1103/physrevb.57.3454

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We calculate the dynamical structure factors of the magnetization plateau state in the $S=\frac{1}{2}$ bond-alternating spin chain with a next-nearest-neighbor interaction. The results show characteristic behaviors depending on the next-nearest-neighbor interaction $\ensuremath{\alpha}$ and the bond alternation \ensuremath{\delta}. We discuss the lower excited states in comparison with the exact excitation spectrums of an effective Hamiltonian. From the finite size effects, characteristics of the lowest excited states are investigated. The dispersionless mode of the lowest excitation appears in adequate sets of $\ensuremath{\alpha}$ and \ensuremath{\delta}, indicating that the lowest excitation is localized spatially and forms an isolated mode below the excitation continuum. We further calculate the static structure factors. The largest intensity is located at $q=\ensuremath{\pi}$ for small $\ensuremath{\delta}$ in fixed \ensuremath{\alpha}. With increasing \ensuremath{\delta}, the wave number of the largest intensity shifts towards $q=\ensuremath{\pi}/2,$ taking the incommensurate value.We calculate the dynamical structure factors of the magnetization plateau state in the $S=\frac{1}{2}$ bond-alternating spin chain with a next-nearest-neighbor interaction. The results show characteristic behaviors depending on the next-nearest-neighbor interaction $\ensuremath{\alpha}$ and the bond alternation \ensuremath{\delta}. We discuss the lower excited states in comparison with the exact excitation spectrums of an effective Hamiltonian. From the finite size effects, characteristics of the lowest excited states are investigated. The dispersionless mode of the lowest excitation appears in adequate sets of $\ensuremath{\alpha}$ and \ensuremath{\delta}, indicating that the lowest excitation is localized spatially and forms an isolated mode below the excitation continuum. We further calculate the static structure factors. The largest intensity is located at $q=\ensuremath{\pi}$ for small $\ensuremath{\delta}$ in fixed \ensuremath{\alpha}. With increasing \ensuremath{\delta}, the wave number of the largest intensity shifts towards $q=\ensuremath{\pi}/2,$ taking the incommensurate value.

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Shaon Sahoo, V. M. L. Durga Prasad Goli, Diptiman Sen +1 more

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ( $J_1^F$ ) and antiferromagnetic ( $J_1^A$ ) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction ( $J_2^F$ ). In this model frustration is induced by the non-zero $J_2^F$ and the effect of dimerization is realized by changing the strength of $J_1^A$ for a fixed value of $J_1^F$ . The model with site spin $s$ behaves like a Haldane spin chain with site spin 2 $s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$ . We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ($J_1^F$) and antiferromagnetic ($J_1^A$) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction ($J_2^F$). In this model frustration is induced by the non-zero $J_2^F$ and the effect of dimerization is realized by changing the strength of $J_1^A$ for a fixed value of $J_1^F$. The model with site spin $s$ behaves like a Haldane spin chain with site spin 2$s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

May 29, 20130 citations

The magnetization process of the

S=1/2

{m}^{z}=1/4,

leading to a plateau, where two degenerate ground states appear. Effective Hamiltonians describing the low-energy physics in the vicinity of the

{m}^{z}=1/4

plateau are also presented. The analogy to metal-insulator transitions is discussed briefly.

We calculate the dynamical structure factors of the magnetization plateau state in the

S=\frac{1}{2}

bond-alternating spin chain with a next-nearest-neighbor interaction. The results show characteristic behaviors depending on the next-nearest-neighbor interaction $\ensuremath{\alpha}$ and the bond alternation \ensuremath{\delta}. We discuss the lower excited states in comparison with the exact excitation spectrums of an effective Hamiltonian. From the finite size effects, characteristics of the lowest excited states are investigated. The dispersionless mode of the lowest excitation appears in adequate sets of $\ensuremath{\alpha}$ and \ensuremath{\delta}, indicating that the lowest excitation is localized spatially and forms an isolated mode below the excitation continuum. We further calculate the static structure factors. The largest intensity is located at $q=\ensuremath{\pi}$ for small $\ensuremath{\delta}$ in fixed \ensuremath{\alpha}. With increasing \ensuremath{\delta}, the wave number of the largest intensity shifts towards $q=\ensuremath{\pi}/2,$ taking the incommensurate value.

We study the ground state properties of the Heisenberg spin-

\frac{1}{2}

chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions using two approximate methods. One of them is the Jordan-Wigner mean-field theory and another approach is based on the transformation of spin operators to Bose ones and on the variational treatment of bosonic Hamiltonian. Both approaches give close results for the ground state energy and the magnetization curve at

T=0

. It is proved that quantum fluctuations change the classical critical exponents in the vicinity of the transition point from the ferromagnetic to the singlet ground state. The magnetization processes display a different behavior in the regions near and far from the transition point. The relation of the obtained results to the experimental magnetization curve in

{\mathrm{Rb}}_{2}{\mathrm{Cu}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}

is discussed.

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (

J_1^F

) and antiferromagnetic (

J_1^A

) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (

J_2^F

). In this model frustration is induced by the non-zero

J_2^F

and the effect of dimerization is realized by changing the strength of

J_1^A

for a fixed value of

J_1^F

. The model with site spin

s

behaves like a Haldane spin chain with site spin 2

s

in the limit of vanishing

J_2^F

and large

J_1^F/J_1^A

. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of

J_1^A-J_2^F

is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.