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

Journal of the Physical Society of Japan

Nature of Ferrimagnetic Ground States in Quantum Spin Models

Shin-ichiro Yoshikawa, Seiji Miyashita

Published Jan 1, 2005• 24 citations
Publisher

Abstract

We will study properties of the ferrimagnetic state depending on types of interaction. In non-frustrated case, the Lieb–Mattis type of ferrimagnetic order appears, where a gap exists between the ground state and the first excited state. On the other hand, in some frustrated lattices, so called non-collinear type of ferrimagnetic order appears, where no gap exists. We will study a model where the type of interaction changes from the former to the latter when one of parameters is varied, and study the dependence of the ground state magnetization on the parameter. We will also study other types of spontaneous magnetization in the ground state in the diamond lattice.

DOI
10.1143/jpsjs.74s.71

Related papers

Frustration-Induced Ferrimagnetism inS= 1/2 Heisenberg Spin Chain

Tokuro Shimokawa, Hiroki Nakano

The ground-state properties of the S=1/2 frustrated Heisenberg spin chain with interactions up to fourth nearest neighbors are investigated by the exact-diagonalization method and density matrix renormalization group method. Our numerical calculations clarify that the ferrimagnetic state is realized in the ground state in spite of the fact that a multi-sublattice structure in the shape of the system is absent. We find that there are two types of ferrimagnetic phases: one is the well-known ferrimagnetic phase of the Lieb-Mattis type and the other is the nontrivial ferrimagnetic phase that is different from that of the Lieb-Mattis type. Our results suggest that a multi-sublattice structure of the shape is not necessarily required for the occurrence of ferrimagnetism.

arXiv:1102.4414•Journal of the Physical Society of Japan•Mar 29, 2011•21 citations

Ferrimagnetism of the Heisenberg model on the Kagome strip lattice

Tokuro Shimokawa, Hiroki Nakano

We study ground-state properties of the S = 1/2 Heisenberg model on the Kagome strip lattice by using exact-diagonalization and density matrix renormalization group methods. When the strength of magnetic frustration is tuned, we find from our numerical calculations that there exists an intermediate phase between the non-magnetic phase and the ferrimagnetic phase of the well-known Lieb-Mattis type and that the local magnetization shows an inocommensurate modulation with long-distance periodicity in the intermediate phase. Since the present model shares the same lattice structure in its inner part with the spatially anisotropic two-dimensional Kagome lattice in which an intermediate phase with a similar behavior is certainly observed, the intermediate phases of these models are the ferrimagnetic one of the unconventional non-Lieb-Mattis type.

Journal of Physics Conference Series•Sep 28, 2011•2 citations

COUPLED CLUSTER TREATMENTS OF QUANTUM MAGNETS: TWO EXAMPLES

Sven E. Krüger, DAMIAN J. J. FARNELL, Johannes Richter

In this article we study the ground-state properties of two square-lattice Heisenberg quantum spin models with competing bonds using a high-order coupled cluster treatment. The first model is a spin-half model with competing nearest-neighbour bonds with and without frustration. We discuss the influence of quantum fluctuations on the ground-state phase diagram and in particular on the nature of the zero-temperature phase transitions from phases with collinear magnetic order at small frustration to phases with noncollinear spiral order at large frustration. The second model is a highly frustrated ferrimagnet, which contains one sublattice (A) entirely populated with spin-one spins and an other sublattice (B) entirely populated with spin-half spins. Sublattice A sites are nearest-neighbours to sublattice B sites and vice versa and frustration is introduced by next-nearest-neighbour bonds. The model shows two collinear ordered phases and a noncollinear phase in which (classically) the spin-one spins are allowed to cant at an angle. Both examples show that the coupled-cluster method is able to describe the zero-temperature transitions well and provides a consistent description of collinear, noncollinear, and disordered phases, for cases in which other standard techniques (e.g. the quantum Monte Carlo technique for spin systems which are frustrated) are not applicable.

International Journal of Modern Physics B•Nov 10, 2003•2 citations

Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism

Xavier Plat, Yohei Fuji, Sylvain Capponi +1 more

The interplay between frustration and quantum fluctuation in magnetic systems is known to be the origin of many exotic states in condensed matter physics. In this paper, we consider a frustrated four-leg spin tube under a magnetic field. This system is a prototype to study the emergence of a nonmagnetic ground state factorizable into local states and the associated order parameter without quantum fluctuation that appears in a wide variety of frustrated systems. The one-dimensional nature of the system allows us to apply various techniques: a path-integral formulation based on the notion of order by disorder, strong-coupling analysis where magnetic excitations are gapped, and density-matrix renormalization group. All methods point toward an interesting property of the ground state in the magnetization plateaus, namely, a quantized value of relative magnetizations between different sublattices (spin imbalance). The ground-state properties can be understood in terms of a direct product of local states on each rung, which is the exact ground state on certain plateaus in the strong-coupling limit.

arXiv:1407.2463•Physical Review B•Feb 6, 2015•12 citations

Ferrimagnetism of the Heisenberg Models on the Quasi-One-Dimensional Kagome Strip Lattices

Tokuro Shimokawa, Hiroki Nakano

We study the ground-state properties of the S=1/2 Heisenberg models on the quasi-onedimensional kagome strip lattices by the exact diagonalization and density matrix renormalization group methods. The models with two different strip widths share the same lattice structure in their inner part with the spatially anisotropic two-dimensional kagome lattice. When there is no magnetic frustration, the well-known Lieb-Mattis ferrimagnetic state is realized in both models. When the strength of magnetic frustration is increased, on the other hand, the Lieb-Mattis-type ferrimagnetism is collapsed. We find that there exists a non-Lieb-Mattis ferrimagnetic state between the Lieb-Mattis ferrimagnetic state and the nonmagnetic ground state. The local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the non-Lieb-Mattis ferrimagnetic state. The intermediate non-Lieb-Mattis ferrimagnetic state occurs irrespective of strip width, which suggests that the intermediate phase of the two-dimensional kagome lattice is also the non-Lieb-Mattis-type ferrimagnetism.

arXiv:1207.6771•Journal of the Physical Society of Japan•Aug 3, 2012•20 citations

Quantum ferrimagnets

Andrey V. Chubukov, K I Ivanova, Plamen Ch. Ivanov +1 more

An instability of a ferromagnetic state in quantum spin systems induced by a two-particle bound-state condensation is shown to produce, for S>2, a ferrimagnetic ground state with a quantized (S Z =S-1) value of spontaneous magnetization per site. For low S, instead, the ground state below the instability has zero net magnetization, while a spontaneous symmetry breaking reveals itself in quadratic, cubic, or both quadratic and cubic correlations for S=1, 2 or 3/2, respectively. The role of quantum fluctuations and the reorientation process in a magnetic field are examined.

Journal of Physics Condensed Matter•Apr 22, 1991•13 citations
We will study properties of the ferrimagnetic state depending on types of interaction. In non-frustrated case, the Lieb–Mattis type of ferrimagnetic order appears, where a gap exists between the ground state and the first excited state. On the other hand, in some frustrated lattices, so called non-collinear type of ferrimagnetic order appears, where no gap exists. We will study a model where the type of interaction changes from the former to the latter when one of parameters is varied, and study the dependence of the ground state magnetization on the parameter. We will also study other types of spontaneous magnetization in the ground state in the diamond lattice.
The ground-state properties of the S=1/2 frustrated Heisenberg spin chain with interactions up to fourth nearest neighbors are investigated by the exact-diagonalization method and density matrix renormalization group method. Our numerical calculations clarify that the ferrimagnetic state is realized in the ground state in spite of the fact that a multi-sublattice structure in the shape of the system is absent. We find that there are two types of ferrimagnetic phases: one is the well-known ferrimagnetic phase of the Lieb-Mattis type and the other is the nontrivial ferrimagnetic phase that is different from that of the Lieb-Mattis type. Our results suggest that a multi-sublattice structure of the shape is not necessarily required for the occurrence of ferrimagnetism.
We study ground-state properties of the S = 1/2 Heisenberg model on the Kagome strip lattice by using exact-diagonalization and density matrix renormalization group methods. When the strength of magnetic frustration is tuned, we find from our numerical calculations that there exists an intermediate phase between the non-magnetic phase and the ferrimagnetic phase of the well-known Lieb-Mattis type and that the local magnetization shows an inocommensurate modulation with long-distance periodicity in the intermediate phase. Since the present model shares the same lattice structure in its inner part with the spatially anisotropic two-dimensional Kagome lattice in which an intermediate phase with a similar behavior is certainly observed, the intermediate phases of these models are the ferrimagnetic one of the unconventional non-Lieb-Mattis type.
In this article we study the ground-state properties of two square-lattice Heisenberg quantum spin models with competing bonds using a high-order coupled cluster treatment. The first model is a spin-half model with competing nearest-neighbour bonds with and without frustration. We discuss the influence of quantum fluctuations on the ground-state phase diagram and in particular on the nature of the zero-temperature phase transitions from phases with collinear magnetic order at small frustration to phases with noncollinear spiral order at large frustration. The second model is a highly frustrated ferrimagnet, which contains one sublattice (A) entirely populated with spin-one spins and an other sublattice (B) entirely populated with spin-half spins. Sublattice A sites are nearest-neighbours to sublattice B sites and vice versa and frustration is introduced by next-nearest-neighbour bonds. The model shows two collinear ordered phases and a noncollinear phase in which (classically) the spin-one spins are allowed to cant at an angle. Both examples show that the coupled-cluster method is able to describe the zero-temperature transitions well and provides a consistent description of collinear, noncollinear, and disordered phases, for cases in which other standard techniques (e.g. the quantum Monte Carlo technique for spin systems which are frustrated) are not applicable.
The interplay between frustration and quantum fluctuation in magnetic systems is known to be the origin of many exotic states in condensed matter physics. In this paper, we consider a frustrated four-leg spin tube under a magnetic field. This system is a prototype to study the emergence of a nonmagnetic ground state factorizable into local states and the associated order parameter without quantum fluctuation that appears in a wide variety of frustrated systems. The one-dimensional nature of the system allows us to apply various techniques: a path-integral formulation based on the notion of order by disorder, strong-coupling analysis where magnetic excitations are gapped, and density-matrix renormalization group. All methods point toward an interesting property of the ground state in the magnetization plateaus, namely, a quantized value of relative magnetizations between different sublattices (spin imbalance). The ground-state properties can be understood in terms of a direct product of local states on each rung, which is the exact ground state on certain plateaus in the strong-coupling limit.
We study the ground-state properties of the S=1/2 Heisenberg models on the quasi-onedimensional kagome strip lattices by the exact diagonalization and density matrix renormalization group methods. The models with two different strip widths share the same lattice structure in their inner part with the spatially anisotropic two-dimensional kagome lattice. When there is no magnetic frustration, the well-known Lieb-Mattis ferrimagnetic state is realized in both models. When the strength of magnetic frustration is increased, on the other hand, the Lieb-Mattis-type ferrimagnetism is collapsed. We find that there exists a non-Lieb-Mattis ferrimagnetic state between the Lieb-Mattis ferrimagnetic state and the nonmagnetic ground state. The local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the non-Lieb-Mattis ferrimagnetic state. The intermediate non-Lieb-Mattis ferrimagnetic state occurs irrespective of strip width, which suggests that the intermediate phase of the two-dimensional kagome lattice is also the non-Lieb-Mattis-type ferrimagnetism.
An instability of a ferromagnetic state in quantum spin systems induced by a two-particle bound-state condensation is shown to produce, for S>2, a ferrimagnetic ground state with a quantized (S Z =S-1) value of spontaneous magnetization per site. For low S, instead, the ground state below the instability has zero net magnetization, while a spontaneous symmetry breaking reveals itself in quadratic, cubic, or both quadratic and cubic correlations for S=1, 2 or 3/2, respectively. The role of quantum fluctuations and the reorientation process in a magnetic field are examined.