arXiv:1710.00508 · Physical review. B./Physical review. B

Magnetization plateaus in the spin- 12 antiferromagnetic Heisenberg model on a kagome-strip chain

Katsuhiro Morita, Takanori Sugimoto, Shigetoshi Sota, Takami Tohyama

Published Jan 16, 2018• 18 citations

Abstract

The spin-$\frac{1}{2}$ Heisenberg model on a kagome lattice is a typical frustrated quantum spin system. The basic structure of a kagome lattice is also present in the kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-$\frac{1}{2}$ Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions using the density-matrix renormalization-group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking translational and/or reflection symmetry spontaneously. The structures are classified by an array of five-site unit cells with specific bond-spin correlations. In a case with a nontrivial plateau, namely a 3/10 plateau, we find long-period magnetic structure with a period of four unit cells.

DOI: 10.1103/physrevb.97.014412

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arXiv:1710.00508 · Physical review. B./Physical review. B

Magnetization plateaus in the spin- 12 antiferromagnetic Heisenberg model on a kagome-strip chain

Katsuhiro Morita, Takanori Sugimoto, Shigetoshi Sota, Takami Tohyama

Published Jan 16, 2018• 18 citations

arXiv HTML PDF

Abstract

The spin-

\frac{1}{2}

Heisenberg model on a kagome lattice is a typical frustrated quantum spin system. The basic structure of a kagome lattice is also present in the kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-

\frac{1}{2}

Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions using the density-matrix renormalization-group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking translational and/or reflection symmetry spontaneously. The structures are classified by an array of five-site unit cells with specific bond-spin correlations. In a case with a nontrivial plateau, namely a 3/10 plateau, we find long-period magnetic structure with a period of four unit cells.

DOI: 10.1103/physrevb.97.014412

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Magnetic Phase Diagrams and Magnetization Plateaus of the Spin-1/2 Antiferromagnetic Heisenberg Model on a Square-Kagome Lattice with Three Nonequivalent Exchange Interactions

Katsuhiro Morita, Takami Tohyama

Magnetization plateaus in quantum spin systems emerges in two-dimensional frustrated systems such as kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on square-kagome lattice is also appropriate for the study of magnetization plateau. Motivated by recent experimental finding of such a square-kagome lattice with nonequivalent three bonds, we investigate the phase diagrams and magnetization plateaus of the lattice by the exact diagonalization method. In addition to previously reported the 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose magnetic structure is characterized by spontaneously broken four-fold rotational symmetry. The plateau appears only in the case of three nonequivalent bonds. We propose the possibility of finding plateaus including the new one.Magnetization plateaus in quantum spin systems emerges in two-dimensional frustrated systems such as kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on square-kagome lattice is also appropriate for the study of magnetization plateau. Motivated by recent experimental finding of such a square-kagome lattice with nonequivalent three bonds, we investigate the phase diagrams and magnetization plateaus of the lattice by the exact diagonalization method. In addition to previously reported the 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose magnetic structure is characterized by spontaneously broken four-fold rotational symmetry. The plateau appears only in the case of three nonequivalent bonds. We propose the possibility of finding plateaus including the new one.

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Theory of the $1/9$ Magnetization Plateau of the Spin- $1/2$ Kagome Heisenberg AntiferromagnetTheory of the $1/9$ Magnetization Plateau of the Spin-$1/2$ Kagome Heisenberg Antiferromagnet

Pratyay Ghosh, Frédéric Mila

We investigate the $1/9$ magnetization plateau of the spin- $1/2$ kagome Heisenberg antiferromagnet using infinite projected entangled-pair states and identify a spin-density-wave state with a $27$ -site unit cell and a lower variational energy than previous approaches. In contrast to higher-magnetization plateaus, which are well described by localized magnons on nonoverlapping hexagons and preserve a sixfold rotational symmetry, the $1/9$ plateau only keeps a threefold rotational symmmetry and consists of a tiling by three types of $9$ -site clusters related by $\pm2π/3$ rotations. These conclusions are supported by a complementary cluster mean-field theory which correctly preserves the symmetry of the higher plateaus but leads to the same spontaneous symmetry breaking for the $1/9$ plateau with a qualitatively similar pattern of nine different local magnetizations.We investigate the $1/9$ magnetization plateau of the spin-$1/2$ kagome Heisenberg antiferromagnet using infinite projected entangled-pair states and identify a spin-density-wave state with a $27$-site unit cell and a lower variational energy than previous approaches. In contrast to higher-magnetization plateaus, which are well described by localized magnons on nonoverlapping hexagons and preserve a sixfold rotational symmetry, the $1/9$ plateau only keeps a threefold rotational symmmetry and consists of a tiling by three types of $9$-site clusters related by $\pm2π/3$ rotations. These conclusions are supported by a complementary cluster mean-field theory which correctly preserves the symmetry of the higher plateaus but leads to the same spontaneous symmetry breaking for the $1/9$ plateau with a qualitatively similar pattern of nine different local magnetizations.

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We analyze the magnetization curve of the spin-1/2 kagome Heisenberg model in a magnetic field. Using state-of-the-art variational wave functions based on neural networks, we confirm the presence of robust magnetization plateaus at $m=1/3$ , $5/9$ and $7/9$ of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a $\sqrt{3}\times \sqrt{3}$ unit cell. Regarding the more challenging $m=1/9$ plateau, we find two competing valence bond crystals depending on the system size, both breaking translation as well as point group symmetries and with a larger $3\times 3$ unit cell. Such quantum states with local modulations of the magnetization average values could be observed experimentally in the near future.We analyze the magnetization curve of the spin-1/2 kagome Heisenberg model in a magnetic field. Using state-of-the-art variational wave functions based on neural networks, we confirm the presence of robust magnetization plateaus at $m=1/3$, $5/9$ and $7/9$ of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a $\sqrt{3}\times \sqrt{3}$ unit cell. Regarding the more challenging $m=1/9$ plateau, we find two competing valence bond crystals depending on the system size, both breaking translation as well as point group symmetries and with a larger $3\times 3$ unit cell. Such quantum states with local modulations of the magnetization average values could be observed experimentally in the near future.

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Katsuhiro Morita, Shigetoshi Sota, Takami Tohyama

Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin- $\frac{1}{2}$ kagome-strip chain, which is one of the frustrated one-dimensional spin systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using the density matrix renormalization group method. We find 15 magnetization-plateau phases, one of which is equivalent to the spin-1 Haldane phase.Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin-$\frac{1}{2}$ kagome-strip chain, which is one of the frustrated one-dimensional spin systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using the density matrix renormalization group method. We find 15 magnetization-plateau phases, one of which is equivalent to the spin-1 Haldane phase.

arXiv:2108.12584Physical review. B./Physical review. BDec 13, 20217 citations

The spin-

\frac{1}{2}

\frac{1}{2}

We study the ground state of the

S=\frac{1}{2}

Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group method with the sine-square deformation. We obtain magnetization plateaus at

M/{M}_{\mathrm{sat}}=0,\frac{1}{4},\frac{3}{8},\frac{1}{2}

, and

\frac{3}{4}

, where

{M}_{\mathrm{sat}}

is the saturated magnetization. The obtained

\frac{3}{4}

plateau state is consistent with the exact result, and the

\frac{1}{2}

plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the

\frac{1}{3}

plateau of the kagome lattice. Different four-spin loop structures are obtained in the

\frac{1}{4}

and

\frac{3}{8}

plateaus but no corresponding states exist in the kagome lattice. The

\frac{3}{8}

plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\ifmmode\times\else\texttimes\fi{}2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.

Theory of the

1/9

Magnetization Plateau of the Spin-

1/2

Kagome Heisenberg Antiferromagnet

We investigate the

1/9

magnetization plateau of the spin-

1/2

kagome Heisenberg antiferromagnet using infinite projected entangled-pair states and identify a spin-density-wave state with a

27

-site unit cell and a lower variational energy than previous approaches. In contrast to higher-magnetization plateaus, which are well described by localized magnons on nonoverlapping hexagons and preserve a sixfold rotational symmetry, the

1/9

plateau only keeps a threefold rotational symmmetry and consists of a tiling by three types of

9

-site clusters related by

\pm2π/3

rotations. These conclusions are supported by a complementary cluster mean-field theory which correctly preserves the symmetry of the higher plateaus but leads to the same spontaneous symmetry breaking for the

1/9

plateau with a qualitatively similar pattern of nine different local magnetizations.

m=1/3

5/9

and

7/9

of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a

\sqrt{3}\times \sqrt{3}

unit cell. Regarding the more challenging

m=1/9

plateau, we find two competing valence bond crystals depending on the system size, both breaking translation as well as point group symmetries and with a larger

3\times 3

unit cell. Such quantum states with local modulations of the magnetization average values could be observed experimentally in the near future.

Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin-

\frac{1}{2}

kagome-strip chain, which is one of the frustrated one-dimensional spin systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using the density matrix renormalization group method. We find 15 magnetization-plateau phases, one of which is equivalent to the spin-1 Haldane phase.