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:0807.0858 · Physical Review B

Vector chiral and multipolar orders in the spin- 1 2 frustrated ferromagnetic chain in magnetic field

Toshiya Hikihara, Lars Kecke, Tsutomu Momoi, Akira Furusaki

Published Oct 6, 2008• 306 citations
arXivHTMLPDF

Abstract

We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor ${J}_{1}$ and antiferromagnetic next-nearest-neighbor ${J}_{2}$ exchange couplings in the presence of magnetic field. We use both numerical approaches (the density-matrix renormalization-group method and exact diagonalization) and effective-field-theory approach and obtain the ground-state phase diagram for wide parameter range of the coupling ratio ${J}_{1}/{J}_{2}$. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferronematic spin correlation and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic $(p=3)$ and quartic $(p=4)$ phases, are formed through binding of $p$ magnons near the saturation fields, showing quasi-LRO of antiferromultipolar spin correlations. The multipolar phases cross over to spin-density-wave phases as the magnetic field is decreased before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., ${\text{LiCuVO}}_{4}$) are discussed.

DOI
10.1103/physrevb.78.144404

Related papers

Vector chiral and multipolar orders in the spin-1/2 ferromagnetic frustrated chain in magnetic field

Takashi Hikihara, Lars Kecke, Tsutomu Momoi +1 more

We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J_1 and antiferromagnetic next-nearest-neighbor J_2 exchange couplings in the presence of magnetic field. We use both numerical approaches (the density matrix renormalization group method and exact diagonalization) and effective field-theory approach, and obtain the ground-state phase diagram for wide parameter range of the coupling ratio J_1/J_2. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferro-nematic spin correlation, and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formed through binding of p magnons near the saturation fields, showing quasi-LRO of antiferro-multipolar spin correlations. The multipolar phases cross over to spin density wave phases as the magnetic field is decreased, before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., LiCuVO_4) are discussed.

•Jul 5, 2008•0 citations

Vector-spin-chirality order in a dimerized frustrated spin- 12 chain

Hiroshi Ueda, Shigeki Onoda

A frustrated spin-$1/2$ XXZ chain model comprising a ferromagnetic nearest-neighbor coupling with the bond alternation, ${J}_{1}(1\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta})<0$, and an antiferromagnetic second-neighbor exchange coupling ${J}_{2}>0$ is studied at zero and weak magnetic fields by means of density-matrix renormalization-group calculations of order parameters, correlation functions, and the entanglement entropy, as well as an Abelian bosonization analysis. At zero magnetic field, the bond alternation $\ensuremath{\delta}>0$ suppresses the gapless phase characterized by a vector-chiral (VC) long-range order (LRO) and a quasi-LRO of an incommensurate spin spiral, whereas this phase occupies a large region in the space of ${J}_{1}/{J}_{2}$ and the easy-plane exchange anisotropy for $\ensuremath{\delta}=0$ [S. Furukawa et al., Phys. Rev. Lett. 105, 257205 (2010)]. Then, four gapped phases are found to appear as the exchange anisotropy varies from the SU(2)-symmetric case to the U(1)-symmetric case: the Haldane dimer (D${}_{+}$) phase with the same sign of the $x,y$- and $z$-component dimer order parameters, two VC dimer (VCD${}_{+}$/VCD${}_{\ensuremath{-}}$) phases with the sign of the $z$-component dimer order parameter being unaltered/reversed, and the even-parity dimer (D${}_{\ensuremath{-}}$) phase. At small magnetic fields, a field-induced ring-exchange interaction, which is proportional to a staggered scalar chirality and a magnetic flux penetrating the associated triangle, drives a transition from the D${}_{\ensuremath{-}}$ phase into a VC-Neel-dimer (VCND) phase, but not from the D${}_{+}$ phase. This VCND phase is stable up to the large magnetic field at which the Zeeman term closes the spin gap. A possible relevance to Rb${}_{2}$Cu${}_{2}$Mo${}_{3}$O${}_{12}$ is discussed.

arXiv:1308.5747•Physical Review B•Jan 10, 2014•11 citations

Emergent multipolar spin correlations in a fluctuating spiral: The frustrated ferromagnetic spin- 1 2 Heisenberg chain in a magnetic field

Julien Sudan, Andreas Lüscher, Andreas Martin Läuchli

We present the phase diagram of the frustrated ferromagnetic $S=\frac{1}{2}$ Heisenberg ${J}_{1}\ensuremath{-}{J}_{2}$ chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states toward spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in two-dimensional $S=\frac{1}{2}$ quantum magnets in a magnetic field.

arXiv:0807.1923•Physical Review B•Oct 7, 2009•238 citations

Interplay of interchain interactions and exchange anisotropy: Stability and fragility of multipolar states in spin- 12 quasi-one-dimensional frustrated helimagnets

Satoshi Nishimoto, Stefan‐Ludwig Drechsler, Roman O. Kuzian +2 more

We quantify the stability of the formation of multipolar states against always present interchain couplings in quasi-one-dimensional spin-$\frac{1}{2}$ chain systems with a frustrating in-chain ${J}_{1}\ensuremath{-}{J}_{2}$ exchange, including parameter regimes that are of direct relevance to many edge-shared cuprate spin-chain compounds. Three representative types of antiferromagnetic interchain coupling and the presence of uniaxial exchange anisotropy are considered. The magnetic phase diagrams are determined by density matrix renormalization group calculations and completed by very accurate analytic and numerical results for the nematic and the dipolar phases employing the hard-core-boson approach. We establish that a sizable interchain coupling has a strong influence on the possible instability of multipolar phases at high magnetic fields in the vicinity of the saturation fields in favor of the usual dipolar one-magnon phase. Moreover, skew interchain couplings strongly affect the pitch of spiral states. Our theoretical results bring to the fore candidate materials close to quantum nematic/triatic ordering.

Physical Review B•Dec 10, 2015•33 citations

Magnetic Field Induced Exotic Phases in Isotropic Frustrated Spin-1/2 chain

Aslam Parvej, Manoranjan Kumar

The frustrated isotropic $J_1-J_2$ model with ferromagnetic $J_1$ and anti-ferromagnetic $J_2$ interactions in presence of an axial magnetic field shows many exotic phases, such as vector chiral and multipolar phases. The existing studies of the phase boundaries of these systems are based on the indirect evidences such as correlation functions {\it etc}. In this paper, the phase boundaries of these exotic phases are calculated based on order parameters and jumps in the magnetization. In the strong magnetic field, $Z_2$ symmetry is broken, therefore, order parameter of the vector chiral phase is calculated using the broken symmetry states. Our results obtained using the modified density matrix renormalization group and exact diagonalization methods, suggest that the vector chiral phase exist only in narrow range of parameter space $J_2/J_1$.

arXiv:1408.6629•Aug 28, 2014•0 citations

COMPETING PHASES IN SPIN-½ J1-J2 CHAIN WITH EASY-PLANE ANISOTROPY

Masahiro Sato, Shunsuke Furukawa, Shigeki Onoda +1 more

We summarize our theoretical findings on the ground-state phase diagram of the spin-½ XXZ chain having competing nearest-neighbor (J1) and antiferromagnetic next-nearest-neighbor (J2) couplings. Our study is mainly concerned with the case of ferromagnetic J1, and the case of antiferromagnetic J1 is briefly reviewed for comparison. The phase diagram contains a rich variety of phases in the plane of J1/J2 versus the XXZ anisotropy Δ: vector-chiral phases, Néel phases, several dimer phases, and Tomonaga–Luttinger liquid phases. We discuss the vector-chiral order that appears for a remarkably wide parameter space, successive Néel-dimer phase transitions, and an emergent nonlocal string order in a narrow region of ferromagnetic J1 side.

arXiv:1101.1374•Modern Physics Letters B•May 23, 2011•30 citations
We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J1{J}_{1}J1​ and antiferromagnetic next-nearest-neighbor J2{J}_{2}J2​ exchange couplings in the presence of magnetic field. We use both numerical approaches (the density-matrix renormalization-group method and exact diagonalization) and effective-field-theory approach and obtain the ground-state phase diagram for wide parameter range of the coupling ratio J1/J2{J}_{1}/{J}_{2}J1​/J2​. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferronematic spin correlation and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic (p=3)(p=3)(p=3) and quartic (p=4)(p=4)(p=4) phases, are formed through binding of ppp magnons near the saturation fields, showing quasi-LRO of antiferromultipolar spin correlations. The multipolar phases cross over to spin-density-wave phases as the magnetic field is decreased before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., LiCuVO4{\text{LiCuVO}}_{4}LiCuVO4​) are discussed.
We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J_1 and antiferromagnetic next-nearest-neighbor J_2 exchange couplings in the presence of magnetic field. We use both numerical approaches (the density matrix renormalization group method and exact diagonalization) and effective field-theory approach, and obtain the ground-state phase diagram for wide parameter range of the coupling ratio J_1/J_2. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferro-nematic spin correlation, and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formed through binding of p magnons near the saturation fields, showing quasi-LRO of antiferro-multipolar spin correlations. The multipolar phases cross over to spin density wave phases as the magnetic field is decreased, before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., LiCuVO_4) are discussed.
A frustrated spin-1/21/21/2 XXZ chain model comprising a ferromagnetic nearest-neighbor coupling with the bond alternation, ${J}_{1}(1\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta})<0$, and an antiferromagnetic second-neighbor exchange coupling J2>0{J}_{2}>0J2​>0 is studied at zero and weak magnetic fields by means of density-matrix renormalization-group calculations of order parameters, correlation functions, and the entanglement entropy, as well as an Abelian bosonization analysis. At zero magnetic field, the bond alternation $\ensuremath{\delta}>0$ suppresses the gapless phase characterized by a vector-chiral (VC) long-range order (LRO) and a quasi-LRO of an incommensurate spin spiral, whereas this phase occupies a large region in the space of J1/J2{J}_{1}/{J}_{2}J1​/J2​ and the easy-plane exchange anisotropy for $\ensuremath{\delta}=0$ [S. Furukawa et al., Phys. Rev. Lett. 105, 257205 (2010)]. Then, four gapped phases are found to appear as the exchange anisotropy varies from the SU(2)-symmetric case to the U(1)-symmetric case: the Haldane dimer (D+{}_{+}+​) phase with the same sign of the x,yx,yx,y- and zzz-component dimer order parameters, two VC dimer (VCD+{}_{+}+​/VCD${}_{\ensuremath{-}}$) phases with the sign of the zzz-component dimer order parameter being unaltered/reversed, and the even-parity dimer (D${}_{\ensuremath{-}}$) phase. At small magnetic fields, a field-induced ring-exchange interaction, which is proportional to a staggered scalar chirality and a magnetic flux penetrating the associated triangle, drives a transition from the D${}_{\ensuremath{-}}$ phase into a VC-Neel-dimer (VCND) phase, but not from the D+{}_{+}+​ phase. This VCND phase is stable up to the large magnetic field at which the Zeeman term closes the spin gap. A possible relevance to Rb2{}_{2}2​Cu2{}_{2}2​Mo3{}_{3}3​O12{}_{12}12​ is discussed.
We present the phase diagram of the frustrated ferromagnetic S=12S=\frac{1}{2}S=21​ Heisenberg ${J}_{1}\ensuremath{-}{J}_{2}$ chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states toward spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in two-dimensional S=12S=\frac{1}{2}S=21​ quantum magnets in a magnetic field.
We quantify the stability of the formation of multipolar states against always present interchain couplings in quasi-one-dimensional spin-12\frac{1}{2}21​ chain systems with a frustrating in-chain ${J}_{1}\ensuremath{-}{J}_{2}$ exchange, including parameter regimes that are of direct relevance to many edge-shared cuprate spin-chain compounds. Three representative types of antiferromagnetic interchain coupling and the presence of uniaxial exchange anisotropy are considered. The magnetic phase diagrams are determined by density matrix renormalization group calculations and completed by very accurate analytic and numerical results for the nematic and the dipolar phases employing the hard-core-boson approach. We establish that a sizable interchain coupling has a strong influence on the possible instability of multipolar phases at high magnetic fields in the vicinity of the saturation fields in favor of the usual dipolar one-magnon phase. Moreover, skew interchain couplings strongly affect the pitch of spiral states. Our theoretical results bring to the fore candidate materials close to quantum nematic/triatic ordering.
The frustrated isotropic J1−J2J_1-J_2J1​−J2​ model with ferromagnetic J1J_1J1​ and anti-ferromagnetic J2J_2J2​ interactions in presence of an axial magnetic field shows many exotic phases, such as vector chiral and multipolar phases. The existing studies of the phase boundaries of these systems are based on the indirect evidences such as correlation functions {\it etc}. In this paper, the phase boundaries of these exotic phases are calculated based on order parameters and jumps in the magnetization. In the strong magnetic field, Z2Z_2Z2​ symmetry is broken, therefore, order parameter of the vector chiral phase is calculated using the broken symmetry states. Our results obtained using the modified density matrix renormalization group and exact diagonalization methods, suggest that the vector chiral phase exist only in narrow range of parameter space J2/J1J_2/J_1J2​/J1​.
We summarize our theoretical findings on the ground-state phase diagram of the spin-½ XXZ chain having competing nearest-neighbor (J1) and antiferromagnetic next-nearest-neighbor (J2) couplings. Our study is mainly concerned with the case of ferromagnetic J1, and the case of antiferromagnetic J1 is briefly reviewed for comparison. The phase diagram contains a rich variety of phases in the plane of J1/J2 versus the XXZ anisotropy Δ: vector-chiral phases, Néel phases, several dimer phases, and Tomonaga–Luttinger liquid phases. We discuss the vector-chiral order that appears for a remarkably wide parameter space, successive Néel-dimer phase transitions, and an emergent nonlocal string order in a narrow region of ferromagnetic J1 side.