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:0709.1423 · Journal of the Physical Society of Japan

Exotic Ground State Phases of S=1/2 Heisenberg Δ-Chain with Ferromagnetic Main Chain

Kazuo Hida

Published Apr 10, 2008• 14 citations
arXivHTMLPDF

Abstract

The ground state phase diagram of the spin-1/2 Heisenberg frustrated $Δ$-chain with a ferromagnetic main chain is investigated. In addition to the ferromagnetic phase, various nonmagnetic ground states are found. If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases. In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which suggest the possibility of a series of phase transitions among different nonmagnetic phases are obtained. Physical pictures of these phases are discussed based on the numerical results.

DOI
10.1143/jpsj.77.044707

Related papers

Exotic ground state phases of S=1/2 heisenberg Delta-chain with ferromagnetic main chain

和男 飛田

The ground state phase diagram of the spin-1/2 Heisenberg frustrated ∆-chain with a ferromagnetic main chain is investigated.In addition to the ferromagnetic phase, various nonmagnetic ground states are found.If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases.In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which suggest the possibility of a series of phase transitions among different nonmagnetic phases are obtained.Physical pictures of these phases are discussed based on the numerical results.

Journal of the Physical Society of Japan•Apr 1, 2008•0 citations

Frustration-induced quantum phases in mixed spin chain with frustrated side chains

Kazuo Hida, Ken'ichi Takano

A mixed Heisenberg spin chain with frustrated side chains is investigated by numerical and perturbational calculations. A frustration-induced quantum partially polarized ferrimagnetic phase and a nonmagnetic spin quadrupolar phase are found adjacent to the conventional Lieb-Mattis-type ferrimagnetic phase or the nonmagnetic singlet cluster solid phases. The partially polarized ferrimagnetic phase has an incommensurate spin structure. Similar structures are commonly found in other frustration-induced partially polarized ferrimagnetic phases. Numerical results also suggest a series of almost critical nonmagnetic ground states in a highly frustrated regime if the side chain spins weakly couple to the main chain.

arXiv:0805.3604•Physical Review B•Aug 11, 2008•31 citations

Frustration-induced quantum phases in mixed spin chain with frustrated side chains

和男 飛田

A mixed Heisenberg spin chain with frustrated side chains is investigated by numerical and perturbational calculations.A frustration-induced quantum partially polarized ferrimagnetic phase and a nonmagnetic spin quadrupolar phase are found adjacent to the conventional Lieb-Mattis-type ferrimagnetic phase or the nonmagnetic singlet cluster solid phases.The partially polarized ferrimagnetic phase has an incommensurate spin structure.Similar structures are commonly found in other frustration-induced partially polarized ferrimagnetic phases.Numerical results also suggest a series of almost critical nonmagnetic ground states in a highly frustrated regime if the side chain spins weakly couple to the main chain.

Physical Review B•Aug 1, 2008•0 citations

Ground-State Phase Diagram of \((1/2,1/2,1)\) Mixed Diamond Chains

Kazuo Hida

The ground-state phases of mixed diamond chains with ($S, τ^{(1)}, τ^{(2)})=(1/2,1/2,1)$, where $S$ is the magnitude of vertex spins, and $τ^{(1)}$ and $τ^{(2)}$ are those of apical spins, are investigated. The two apical spins in each unit cell are coupled by an exchange coupling $λ$. The vertex spins are coupled with the top and bottom apical spins by exchange couplings $1+δ$ and $1-δ$, respectively. Although this model has an infinite number of local conservation laws for $δ=0$, they are lost for finite $δ$. The ground-state phase diagram is determined using the numerical exact diagonalization and DMRG method in addition to the analytical approximations in various limiting cases. The phase diagram consists of a nonmagnetic phase and several kinds of ferrimagnetic phases. We find two different ferrimagnetic phases without spontaneous translational symmetry breakdown. It is also found that the quantized ferrimagnetic phases with large spatial periodicities present for $δ=0$ are easily destroyed by small $δ$ and replaced by a partial ferrimagnetic phase. The nonmagnetic phase is considered to be a gapless Tomonaga-Luttinger liquid phase based on the recently extended Lieb-Schultz-Mattis theorem to the site-reflection invariant spin chains and numerical diagonalization results.

arXiv:2312.01630•Journal of the Physical Society of Japan•Mar 8, 2024•2 citations

Ground-State Phase Diagram of S = 2 Heisenberg Chains with Alternating Single-Site Anisotropy

Kazuo Hida

The ground-state phase diagram of $S=2$ antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-$D$, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.

arXiv:1310.8586•Journal of the Physical Society of Japan•Feb 14, 2014•3 citations

Ground-state phase diagram of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with anisotropy

Kazuo Hida

The ground state of the ferromagnetic-antiferromagnetic alternating spin-1/2 Heisenberg chain is studied with Ising-type anisotropy on the ferromagnetic bond. This model tends to the spin-1 antiferromagnetic Heisenberg chain with on-site anisotropy in the limit of strong ferromagnetic bond. It is found that the Haldane-gap phase, the large-D phase, and the two types of N\'eel phases appear as the ground state of this model. The duality relations between these four phases are proved for several limiting cases. The string order parameter characterizing the large-D phase is introduced based on these duality relations. The ground-state phase diagram is determined by the numerical diagonalization of the finite-size system.

Physical review. B, Condensed matter•Oct 1, 1992•81 citations
The ground state phase diagram of the spin-1/2 Heisenberg frustrated ΔΔΔ-chain with a ferromagnetic main chain is investigated. In addition to the ferromagnetic phase, various nonmagnetic ground states are found. If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases. In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which suggest the possibility of a series of phase transitions among different nonmagnetic phases are obtained. Physical pictures of these phases are discussed based on the numerical results.
The ground state phase diagram of the spin-1/2 Heisenberg frustrated ∆-chain with a ferromagnetic main chain is investigated.In addition to the ferromagnetic phase, various nonmagnetic ground states are found.If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases.In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which suggest the possibility of a series of phase transitions among different nonmagnetic phases are obtained.Physical pictures of these phases are discussed based on the numerical results.
A mixed Heisenberg spin chain with frustrated side chains is investigated by numerical and perturbational calculations. A frustration-induced quantum partially polarized ferrimagnetic phase and a nonmagnetic spin quadrupolar phase are found adjacent to the conventional Lieb-Mattis-type ferrimagnetic phase or the nonmagnetic singlet cluster solid phases. The partially polarized ferrimagnetic phase has an incommensurate spin structure. Similar structures are commonly found in other frustration-induced partially polarized ferrimagnetic phases. Numerical results also suggest a series of almost critical nonmagnetic ground states in a highly frustrated regime if the side chain spins weakly couple to the main chain.
A mixed Heisenberg spin chain with frustrated side chains is investigated by numerical and perturbational calculations.A frustration-induced quantum partially polarized ferrimagnetic phase and a nonmagnetic spin quadrupolar phase are found adjacent to the conventional Lieb-Mattis-type ferrimagnetic phase or the nonmagnetic singlet cluster solid phases.The partially polarized ferrimagnetic phase has an incommensurate spin structure.Similar structures are commonly found in other frustration-induced partially polarized ferrimagnetic phases.Numerical results also suggest a series of almost critical nonmagnetic ground states in a highly frustrated regime if the side chain spins weakly couple to the main chain.
Ground-State Phase Diagram of (1/2,1/2,1)(1/2,1/2,1)(1/2,1/2,1) Mixed Diamond Chains
The ground-state phases of mixed diamond chains with (S,τ(1),τ(2))=(1/2,1/2,1)S, τ^{(1)}, τ^{(2)})=(1/2,1/2,1)S,τ(1),τ(2))=(1/2,1/2,1), where SSS is the magnitude of vertex spins, and τ(1)τ^{(1)}τ(1) and τ(2)τ^{(2)}τ(2) are those of apical spins, are investigated. The two apical spins in each unit cell are coupled by an exchange coupling λλλ. The vertex spins are coupled with the top and bottom apical spins by exchange couplings 1+δ1+δ1+δ and 1−δ1-δ1−δ, respectively. Although this model has an infinite number of local conservation laws for δ=0δ=0δ=0, they are lost for finite δδδ. The ground-state phase diagram is determined using the numerical exact diagonalization and DMRG method in addition to the analytical approximations in various limiting cases. The phase diagram consists of a nonmagnetic phase and several kinds of ferrimagnetic phases. We find two different ferrimagnetic phases without spontaneous translational symmetry breakdown. It is also found that the quantized ferrimagnetic phases with large spatial periodicities present for δ=0δ=0δ=0 are easily destroyed by small δδδ and replaced by a partial ferrimagnetic phase. The nonmagnetic phase is considered to be a gapless Tomonaga-Luttinger liquid phase based on the recently extended Lieb-Schultz-Mattis theorem to the site-reflection invariant spin chains and numerical diagonalization results.
The ground-state phase diagram of S=2S=2S=2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-DDD, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
The ground state of the ferromagnetic-antiferromagnetic alternating spin-1/2 Heisenberg chain is studied with Ising-type anisotropy on the ferromagnetic bond. This model tends to the spin-1 antiferromagnetic Heisenberg chain with on-site anisotropy in the limit of strong ferromagnetic bond. It is found that the Haldane-gap phase, the large-D phase, and the two types of N\'eel phases appear as the ground state of this model. The duality relations between these four phases are proved for several limiting cases. The string order parameter characterizing the large-D phase is introduced based on these duality relations. The ground-state phase diagram is determined by the numerical diagonalization of the finite-size system.