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/0610103 · Physical Review B

Zigzag spin- S chain near the ferromagnet-antiferromagnet transition point

Д. В. Дмитриев, V. Ya. Krivnov, Johannes Richter

Published Jan 18, 2007• 33 citations
arXivHTMLPDF

Abstract

The properties of the ferromagnetic frustrated spin-$S$ one-dimensional Heisenberg model in the vicinity of the transition point from the ferromagnetic to the singlet ground state are studied using the perturbation theory (PT) in small parameter characterizing the deviation from the transition point. The critical exponents defining the behavior of the ground-state energy and spin correlation functions are determined using scaling estimates of infrared divergencies of the PT. It is shown that the quantum fluctuations for $s=1∕2$ are sufficiently strong to change the classical critical exponents, while for spin systems with $s\ensuremath{\geqslant}1$ the critical exponents remain classical. The dimerization in the singlet phase near the transition point is discussed.

DOI
10.1103/physrevb.75.014424

Related papers

The ground state energy of the frustrated ferromagnetic spin chain near the transition point

Ren-Gui Zhu

The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is first bosonized by using the linear spin wave approximation, and then is treated by using the Green's function approach. An integral expression of the quantum correction to the classical ground state energy is derived. The critical behavior of the ground state energy in the vicinity of the transition point from the ferromagnetic to the singlet ground state is analyzed by numerical calculation, and the result is $-8γ^2$.

arXiv:1104.2946•Apr 15, 2011•0 citations

Frustrated ferromagnetic spin- 12 chain in a magnetic field

Д. В. Дмитриев, V. Ya. Krivnov

We study the ground state properties of the Heisenberg spin-$\frac{1}{2}$ chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions using two approximate methods. One of them is the Jordan-Wigner mean-field theory and another approach is based on the transformation of spin operators to Bose ones and on the variational treatment of bosonic Hamiltonian. Both approaches give close results for the ground state energy and the magnetization curve at $T=0$. It is proved that quantum fluctuations change the classical critical exponents in the vicinity of the transition point from the ferromagnetic to the singlet ground state. The magnetization processes display a different behavior in the regions near and far from the transition point. The relation of the obtained results to the experimental magnetization curve in ${\mathrm{Rb}}_{2}{\mathrm{Cu}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}$ is discussed.

arXiv:cond-mat/0507301•Physical Review B•Jan 3, 2006•55 citations

Frustrated Ferromagnetic Spin Chain near the Transition Point

Ren-Gui Zhu

The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is firstly rewritten in a form with rotated spin operators, then bosonized by using the linear spin wave approximation and then treated by using the Green function approach. An integral expression of the quantum correction to the classical ground state energy is derived. The critical behavior of the ground state energy in the vicinity of the transition point from the ferromagnetic to the singlet ground state is analyzed by numerical calculation and the result is −8γ 2 .

Chinese Physics Letters•Sep 1, 2011•2 citations

Numerical study of the frustrated ferromagnetic spin-\frac {1}{2} chain

S. Mahdavifar

The ground state phase diagram of the frustrated ferromagnetic spin- chain is investigated using the exact diagonalization technique. It is shown that there is a jump in the spontaneous magnetization and the ground state of the system undergoes a phase transition from a ferromagnetic phase to a phase with dimer ordering between next-nearest-neighbor spins. Near the quantum transition point, the critical behavior of the ground state energy is analyzed numerically. Using a practical finite-size scaling approach, the critical exponent of the ground state energy is computed. Our numerical results are in good agreement with the results obtained with other theoretical approaches.

arXiv:0807.2094•Journal of Physics Condensed Matter•Jul 31, 2008•19 citations

Frustrated quantum magnetism in the Kondo lattice on the zigzag ladder

Matthias Peschke, Roman Rausch, Michael Potthoff

The interplay between the Kondo effect, indirect magnetic interaction, and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group, the ground-state and various short- and long-range spin- and density-correlation functions are calculated for the model at half filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$, where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at ${J}_{\mathrm{c}}^{\mathrm{dim}}\ensuremath{\approx}0.89t$ frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a ${90}^{\ensuremath{\circ}}$ quantum spin spiral with quasi-long-range order at ${J}_{\mathrm{c}}^{\mathrm{mag}}\ensuremath{\approx}0.84t$. The quantum-critical point is characterized by a closure of the spin gap (with decreasing $J$) and a divergence of the spin-correlation length and of the spin-structure factor $S(q)$ at wave vector $q=\ensuremath{\pi}/2$. This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all $J>0$ at half filling.

arXiv:1709.05642•Physical review. B./Physical review. B•Mar 12, 2018•7 citations

Weakly anisotropic frustrated zigzag spin chain

Д. В. Дмитриев, V. Ya. Krivnov

The frustrated spin-$1∕2$ model with weakly anisotropic ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchanges is studied with use of variational mean-field approach, scaling estimates of the infrared divergencies in the perturbation theory and finite-size calculations. The ground-state phase diagram of this model contains three phases: the ferromagnetic phase, the commensurate spin-fluid phase, and the incommensurate phase. The nontrivial behavior of the boundaries between these phases and the character of the phase transitions in case of weak anisotropy are determined.

arXiv:0708.3555•Physical Review B•Jan 2, 2008•48 citations
The properties of the ferromagnetic frustrated spin-SSS one-dimensional Heisenberg model in the vicinity of the transition point from the ferromagnetic to the singlet ground state are studied using the perturbation theory (PT) in small parameter characterizing the deviation from the transition point. The critical exponents defining the behavior of the ground-state energy and spin correlation functions are determined using scaling estimates of infrared divergencies of the PT. It is shown that the quantum fluctuations for s=1∕2s=1∕2s=1∕2 are sufficiently strong to change the classical critical exponents, while for spin systems with s\ensuremath⩾1s\ensuremath{\geqslant}1s\ensuremath⩾1 the critical exponents remain classical. The dimerization in the singlet phase near the transition point is discussed.
The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is first bosonized by using the linear spin wave approximation, and then is treated by using the Green's function approach. An integral expression of the quantum correction to the classical ground state energy is derived. The critical behavior of the ground state energy in the vicinity of the transition point from the ferromagnetic to the singlet ground state is analyzed by numerical calculation, and the result is −8γ2-8γ^2−8γ2.
We study the ground state properties of the Heisenberg spin-12\frac{1}{2}21​ chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions using two approximate methods. One of them is the Jordan-Wigner mean-field theory and another approach is based on the transformation of spin operators to Bose ones and on the variational treatment of bosonic Hamiltonian. Both approaches give close results for the ground state energy and the magnetization curve at T=0T=0T=0. It is proved that quantum fluctuations change the classical critical exponents in the vicinity of the transition point from the ferromagnetic to the singlet ground state. The magnetization processes display a different behavior in the regions near and far from the transition point. The relation of the obtained results to the experimental magnetization curve in Rb2Cu2Mo3O12{\mathrm{Rb}}_{2}{\mathrm{Cu}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}Rb2​Cu2​Mo3​O12​ is discussed.
The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is firstly rewritten in a form with rotated spin operators, then bosonized by using the linear spin wave approximation and then treated by using the Green function approach. An integral expression of the quantum correction to the classical ground state energy is derived. The critical behavior of the ground state energy in the vicinity of the transition point from the ferromagnetic to the singlet ground state is analyzed by numerical calculation and the result is −8γ 2 .
The ground state phase diagram of the frustrated ferromagnetic spin- chain is investigated using the exact diagonalization technique. It is shown that there is a jump in the spontaneous magnetization and the ground state of the system undergoes a phase transition from a ferromagnetic phase to a phase with dimer ordering between next-nearest-neighbor spins. Near the quantum transition point, the critical behavior of the ground state energy is analyzed numerically. Using a practical finite-size scaling approach, the critical exponent of the ground state energy is computed. Our numerical results are in good agreement with the results obtained with other theoretical approaches.
The interplay between the Kondo effect, indirect magnetic interaction, and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group, the ground-state and various short- and long-range spin- and density-correlation functions are calculated for the model at half filling as a function of the antiferromagnetic Kondo interaction down to J=0.3tJ=0.3tJ=0.3t, where ttt is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-JJJ limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at ${J}_{\mathrm{c}}^{\mathrm{dim}}\ensuremath{\approx}0.89t$ frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a ${90}^{\ensuremath{\circ}}$ quantum spin spiral with quasi-long-range order at ${J}_{\mathrm{c}}^{\mathrm{mag}}\ensuremath{\approx}0.84t$. The quantum-critical point is characterized by a closure of the spin gap (with decreasing JJJ) and a divergence of the spin-correlation length and of the spin-structure factor S(q)S(q)S(q) at wave vector $q=\ensuremath{\pi}/2$. This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all J>0J>0J>0 at half filling.
The frustrated spin-1∕21∕21∕2 model with weakly anisotropic ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchanges is studied with use of variational mean-field approach, scaling estimates of the infrared divergencies in the perturbation theory and finite-size calculations. The ground-state phase diagram of this model contains three phases: the ferromagnetic phase, the commensurate spin-fluid phase, and the incommensurate phase. The nontrivial behavior of the boundaries between these phases and the character of the phase transitions in case of weak anisotropy are determined.