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/9910057 · Physical review. B, Condensed matter

Magnetization plateaus as insulator-superfluid transitions in quantum spin systems

Tsutomu Momoi, Keisuke Totsuka

Published Feb 1, 2000• 100 citations
arXivHTMLPDF

Abstract

We study the magnetization process in two-dimensional $S=1/2$ spin systems, to discuss the appearance of a plateau structure. The following three cases are considered: (1) the Heisenberg antiferromagnet and multiple-spin exchange model on the triangular lattice, (2) the Shastry-Sutherland-type lattice [which is a possible model for ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}],$ (3) the 1/5-depleted lattice (for ${\mathrm{CaV}}_{4}{\mathrm{O}}_{9}).$ We find in these systems that magnetization plateaus can appear owing to a transition from superfluid to a Mott insulator of magnetic excitations. The plateau states have charge-density-wave order of the excitations. The magnetizations of the plateaus depend on components of the magnetic excitations, the range of the repulsive interaction, and the geometry of the lattice.

DOI
10.1103/physrevb.61.3231

Related papers

Phases and magnetization process of an anisotropic Shastry-Sutherland model

Zi Yang Meng, Stefan Weßel

We examine ground-state properties of the spin-1/2 easy-axis Heisenberg model on the Shastry-Sutherland lattice with ferromagnetic transverse spin exchange using quantum Monte Carlo and degenerate perturbation theory. For vanishing transverse exchange, the model reduces to an antiferromagnetic Ising model that, besides N\'eel order, harbors regions of extensive ground-state degeneracy. In the quantum regime, we find a dimerized phase of triplet states separated from the N\'eel ordered phase by a superfluid. The quantum phase transitions between these phases are characterized. The magnetization process shows a magnetization plateau at 1/3 of the saturation value, which persists down to the Ising limit, and a further plateau at 1/2 only in the quantum regime. For both plateaus, we determine the crystalline patterns of the localized triplet excitations. No further plateaus or supersolid phases are found in this model.

arXiv:0808.3104•Physical Review B•Dec 18, 2008•50 citations

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.

arXiv:1802.00232•Journal of the Physical Society of Japan•Mar 14, 2018•28 citations

Exotic magnetization plateaus in a quasi-two-dimensional Shastry-Sutherland model

G. R. Foltin, Salvatore R. Manmana, Kai Phillip Schmidt

We find unconventional Mott insulators in a quasi-2D version of the Shastry-Sutherland model in a magnetic field. In our realization on a four-leg tube geometry, these are stabilized by correlated hopping of localized magnetic excitations. Using perturbative continuous unitary transformations (pCUTs, plus classical approximation or exact diagonalization) and the density matrix renormalisation group method (DMRG), we identify prominent magnetization plateaus at magnetizations $M=1/8,3/16,1/4$, and $1/2$. While the plateau at $M=1/4$ can be understood in a semiclassical fashion in terms of diagonal stripes, the plateau at $M=1/8$ displays highly entangled wheels in the transverse direction of the tube. Finally, the $M=3/16$ plateau is most likely to be viewed as a classical 1/8 structure on which additional triplets are fully delocalized around the tube. The classical approximation of the effective model fails to describe all these plateau structures which benefit from correlated hopping. We relate our findings to the full 2D system, which is the underlying model for the frustrated quantum magnet $\mathrm{SrCu}{({\mathrm{BO}}_{3})}_{2}$.

arXiv:1405.3260•Physical Review B•Sep 3, 2014•23 citations

Magnetization plateaus in frustrated antiferromagnetic quantum spin models

A. Honecker, J. Schulenburg, Johannes Richter

Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) for up to N = 40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagomé lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.

arXiv:cond-mat/0309425•Journal of Physics Condensed Matter•Mar 4, 2004•185 citations

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

Katsuhiro Morita, Takanori Sugimoto, Shigetoshi Sota +1 more

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.

arXiv:1710.00508•Physical review. B./Physical review. B•Jan 16, 2018•18 citations

Exact magnetization plateaus and phase transitions in spin- S Heisenberg antiferromagnets in arbitrary dimensions

V. Ravi Chandra, Naveen Surendran

We generalize a class of Heisenberg antiferromagnets in one, two, and three dimensions, which have been shown to exhibit magnetization plateaus for spin-$\frac{1}{2}$. In a certain parameter range of the general model, which is formally defined in $D$ dimensions, we obtain the exact ground state(s) in the presence of an external magnetic field for arbitrary values of spin. In this range, the magnetization remains a constant as a function of the external field, except at some special values of the field where there is a jump from one plateau to the next. The plateaus are formed at certain specific fractions of the full magnetization which are determined by the spin and the lattice. Our general spin-$S$ result reproduces the known cases for spin-$\frac{1}{2}$ in various lattices. Furthermore, we argue that outside the exact regime, the mechanism for the plateau formation is different. This results in first order phase transitions along some of the plateaus as the coupling constant is varied. We rigorously show the existence of such transitions for some particular cases. Finally, we numerically analyze a spin-$1$ model in one dimension using exact diagonalization to obtain its complete phase diagram. It agrees with our analytic results.

arXiv:cond-mat/0604258•Physical Review B•Jul 21, 2006•13 citations
We study the magnetization process in two-dimensional S=1/2S=1/2S=1/2 spin systems, to discuss the appearance of a plateau structure. The following three cases are considered: (1) the Heisenberg antiferromagnet and multiple-spin exchange model on the triangular lattice, (2) the Shastry-Sutherland-type lattice [which is a possible model for SrCu2(BO3)2],{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}],SrCu2​(BO3​)2​], (3) the 1/5-depleted lattice (for CaV4O9).{\mathrm{CaV}}_{4}{\mathrm{O}}_{9}).CaV4​O9​). We find in these systems that magnetization plateaus can appear owing to a transition from superfluid to a Mott insulator of magnetic excitations. The plateau states have charge-density-wave order of the excitations. The magnetizations of the plateaus depend on components of the magnetic excitations, the range of the repulsive interaction, and the geometry of the lattice.
We examine ground-state properties of the spin-1/2 easy-axis Heisenberg model on the Shastry-Sutherland lattice with ferromagnetic transverse spin exchange using quantum Monte Carlo and degenerate perturbation theory. For vanishing transverse exchange, the model reduces to an antiferromagnetic Ising model that, besides N\'eel order, harbors regions of extensive ground-state degeneracy. In the quantum regime, we find a dimerized phase of triplet states separated from the N\'eel ordered phase by a superfluid. The quantum phase transitions between these phases are characterized. The magnetization process shows a magnetization plateau at 1/3 of the saturation value, which persists down to the Ising limit, and a further plateau at 1/2 only in the quantum regime. For both plateaus, we determine the crystalline patterns of the localized triplet excitations. No further plateaus or supersolid phases are found in this model.
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.
We find unconventional Mott insulators in a quasi-2D version of the Shastry-Sutherland model in a magnetic field. In our realization on a four-leg tube geometry, these are stabilized by correlated hopping of localized magnetic excitations. Using perturbative continuous unitary transformations (pCUTs, plus classical approximation or exact diagonalization) and the density matrix renormalisation group method (DMRG), we identify prominent magnetization plateaus at magnetizations M=1/8,3/16,1/4M=1/8,3/16,1/4M=1/8,3/16,1/4, and 1/21/21/2. While the plateau at M=1/4M=1/4M=1/4 can be understood in a semiclassical fashion in terms of diagonal stripes, the plateau at M=1/8M=1/8M=1/8 displays highly entangled wheels in the transverse direction of the tube. Finally, the M=3/16M=3/16M=3/16 plateau is most likely to be viewed as a classical 1/8 structure on which additional triplets are fully delocalized around the tube. The classical approximation of the effective model fails to describe all these plateau structures which benefit from correlated hopping. We relate our findings to the full 2D system, which is the underlying model for the frustrated quantum magnet SrCu(BO3)2\mathrm{SrCu}{({\mathrm{BO}}_{3})}_{2}SrCu(BO3​)2​.
Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) for up to N = 40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagomé lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.
The spin-12\frac{1}{2}21​ 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-12\frac{1}{2}21​ 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.
We generalize a class of Heisenberg antiferromagnets in one, two, and three dimensions, which have been shown to exhibit magnetization plateaus for spin-12\frac{1}{2}21​. In a certain parameter range of the general model, which is formally defined in DDD dimensions, we obtain the exact ground state(s) in the presence of an external magnetic field for arbitrary values of spin. In this range, the magnetization remains a constant as a function of the external field, except at some special values of the field where there is a jump from one plateau to the next. The plateaus are formed at certain specific fractions of the full magnetization which are determined by the spin and the lattice. Our general spin-SSS result reproduces the known cases for spin-12\frac{1}{2}21​ in various lattices. Furthermore, we argue that outside the exact regime, the mechanism for the plateau formation is different. This results in first order phase transitions along some of the plateaus as the coupling constant is varied. We rigorously show the existence of such transitions for some particular cases. Finally, we numerically analyze a spin-111 model in one dimension using exact diagonalization to obtain its complete phase diagram. It agrees with our analytic results.