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:0805.3872 · Journal of the Physical Society of Japan

On Calculation of Vector Spin Chirality for Zigzag Spin Chains

Kouichi Okunishi

Published Nov 10, 2008• 42 citations
arXivHTMLPDF

Abstract

We calculate the vector spin chirality for $S=1/2$ zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the $S=1/2$ zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.

DOI
10.1143/jpsj.77.114004

Related papers

Chirality in spin- 12 zigzag XY chain: Low-temperature density-matrix renormalization group study

Takanori Sugimoto, Shigetoshi Sota, Takami Tohyama

We study spin chirality for a spin-$\frac{1}{2}$ zigzag $XY$ chain at low temperature by applying a low-temperature density-matrix renormalization group technique. We calculate temperature dependence of dynamical and static correlations of the chirality. In a chiral phase, chiral long-range order at zero temperature disappears at finite temperature, consistent with the fact that there is no long-range order at finite temperature in one-dimensional systems with short-range interactions. In a dimer phase next to the chiral phase, we find an enhancement of static chiral correlation as well as spin correlation with increasing temperature. The enhancement corresponds to the increase in spectral weight inside a gap in the dynamical chiral-correlation function. This temperature-induced chiral correlation is a demonstration of the presence of a chiral state in excited states.

arXiv:1004.1486•Physical Review B•Jul 26, 2010•3 citations

Vector chiral order in frustrated spin chains

Ian P. McCulloch, R. Kube, M. Kurz +3 more

By means of a numerical analysis using a non-Abelian symmetry realization of the density matrix renormalization group, we study the behavior of vector chirality correlations in isotropic frustrated chains of spin $S=1$ and $S=1∕2$, subject to a strong external magnetic field. It is shown that the field induces a phase with spontaneously broken chiral symmetry, in line with earlier theoretical predictions. We present results on the field dependence of the order parameter and the critical exponents.

arXiv:0712.3050•Physical Review B•Mar 6, 2008•54 citations

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

Low-temperature density matrix renormalization group study on spin-1/2 frustrated spin chains

Shigetoshi Sota, Takami Tohyama

We study the temperature dependence of the dynamical correlation function of the vector spin chirality on spin-1/2 zigzag XY spin chains by using the low-temperature dynamical density matrix renormalization group that we have developed recently. At zero temperature, gapless and gapful excitations of the chiralily are confirmed for systems with and without the chiral order, respectively. At finite temperatures, we find in the gapful system a characteristic temperature where the low-energy dynamical chirality correlation changes dramatically. This is in contrast to the system with the order where the correlation changes smoothly with temperature.

Journal of Physics Conference Series•Jan 1, 2010•3 citations

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

Toshiya 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 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.

arXiv:0807.0858•Physical Review B•Oct 6, 2008•306 citations

Competing interactions and spin-vector chirality in spin chains

E. Vernek, O. Ávalos-Ovando, Sergio E. Ulloa

Studies of competing orders in one-dimensional magnetic chains have attracted considerable attention in recent years, as the presence of distant-neighbor Heisenberg interactions is found to allow interesting quantum phase transitions. We investigate here the role of spin-orbit effects by considering spin-1/2 chains in the presence of both collinear and noncollinear interactions. By employing exact diagonalization and density matrix renormalization group calculations we investigate the rich phase diagram of this system. We find transitions from collinear to transverse magnetic correlated order as the strength of the noncollinear coupling increases, accompanied by a jump in the vector spin chirality order parameter of the system. This shows that tuning interactions allows control of the onset of sizable vector spin chirality in a system, which may be used to transmit information down the chain. We investigate the characteristic structure of the distinct phases and explore their possible physical implementation in different materials systems.

arXiv:2003.03322•Physical review. B./Physical review. B•Nov 16, 2020•6 citations
We calculate the vector spin chirality for S=1/2S=1/2S=1/2 zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the S=1/2S=1/2S=1/2 zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.
We study spin chirality for a spin-12\frac{1}{2}21​ zigzag XYXYXY chain at low temperature by applying a low-temperature density-matrix renormalization group technique. We calculate temperature dependence of dynamical and static correlations of the chirality. In a chiral phase, chiral long-range order at zero temperature disappears at finite temperature, consistent with the fact that there is no long-range order at finite temperature in one-dimensional systems with short-range interactions. In a dimer phase next to the chiral phase, we find an enhancement of static chiral correlation as well as spin correlation with increasing temperature. The enhancement corresponds to the increase in spectral weight inside a gap in the dynamical chiral-correlation function. This temperature-induced chiral correlation is a demonstration of the presence of a chiral state in excited states.
By means of a numerical analysis using a non-Abelian symmetry realization of the density matrix renormalization group, we study the behavior of vector chirality correlations in isotropic frustrated chains of spin S=1S=1S=1 and S=1∕2S=1∕2S=1∕2, subject to a strong external magnetic field. It is shown that the field induces a phase with spontaneously broken chiral symmetry, in line with earlier theoretical predictions. We present results on the field dependence of the order parameter and the critical exponents.
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.
We study the temperature dependence of the dynamical correlation function of the vector spin chirality on spin-1/2 zigzag XY spin chains by using the low-temperature dynamical density matrix renormalization group that we have developed recently. At zero temperature, gapless and gapful excitations of the chiralily are confirmed for systems with and without the chiral order, respectively. At finite temperatures, we find in the gapful system a characteristic temperature where the low-energy dynamical chirality correlation changes dramatically. This is in contrast to the system with the order where the correlation changes smoothly with temperature.
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.
Studies of competing orders in one-dimensional magnetic chains have attracted considerable attention in recent years, as the presence of distant-neighbor Heisenberg interactions is found to allow interesting quantum phase transitions. We investigate here the role of spin-orbit effects by considering spin-1/2 chains in the presence of both collinear and noncollinear interactions. By employing exact diagonalization and density matrix renormalization group calculations we investigate the rich phase diagram of this system. We find transitions from collinear to transverse magnetic correlated order as the strength of the noncollinear coupling increases, accompanied by a jump in the vector spin chirality order parameter of the system. This shows that tuning interactions allows control of the onset of sizable vector spin chirality in a system, which may be used to transmit information down the chain. We investigate the characteristic structure of the distinct phases and explore their possible physical implementation in different materials systems.