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/0605191 · Physical Review B

Antiferromagnetic and spin-gap phases of the anisotropic Kondo necklace model

A. Langari, Peter Thalmeier

Published Jul 31, 2006• 22 citations
arXivHTMLPDF

Abstract

We have studied the effect of anisotropies on the quantum phase transition of the Kondo necklace model in dimensions $D=1$, 2, and 3. Both the anisotropy $\ensuremath{\delta}$ of the intersite interaction term and anisotropy $\ensuremath{\Delta}$ of the on-site Kondo interaction have been included. We use a bond operator method with constraints implemented in mean-field approximation. Starting from the paramagnetic phase we determine the critical ratio ${(t∕J)}_{c}$ of the quantum critical point and associated scaling exponents of the Kondo-singlet gap. We show that in the case of easy-axis type anisotropy $\ensuremath{\delta}>1$ a qualitatively different behavior in comparison to the conventional Kondo necklace model with $(\ensuremath{\delta},\ensuremath{\Delta})=(0,1)$ appears. We have also obtained the antiferromagnetic order parameter in the long range ordered phase for $t>{t}_{c}$.

DOI
10.1103/physrevb.74.024431

Related papers

Green’s function approach to quantum criticality in the anisotropic Kondo necklace model

Hamed Rezania, A. Langari, Peter Thalmeier

We have studied the quantum phase transition between the antiferromagnetic and spin liquid phases for the two-dimensional anisotropic Kondo necklace model. The bond operator formalism has been implemented to transform the spin Hamiltonian to a bosonic one. We have used the Green's function approach including a hard core repulsion to find the low energy excitation spectrum of the model. The bosonic excitations become gapless at the quantum critical point where the phase transition from the Kondo singlet state to long range antiferromagnetic order takes place. We have studied the effect of both intersite $(\ensuremath{\delta})$ and local $(\ensuremath{\Delta})$ anisotropies on the critical point and on the critical exponent of the excitation gap in the paramagnetic phase. We have also compared our results with previous bond operator mean field calculations.

arXiv:0802.0736•Physical Review B•Mar 28, 2008•22 citations

Phase diagram of the one-dimensional anisotropic Kondo-necklace model

Samiyeh Mahmoudian, A. Langari

The one-dimensional anisotropic Kondo-necklace model has been studied by several methods. It is shown that a mean field approach fails to gain the correct phase diagram for the Ising-type anisotropy. We then applied the spin wave theory which is justified for the anisotropic case. We have derived the phase diagram between the antiferromagnetic long range order and the Kondo singlet phases. We have found that the exchange interaction $(J)$ between the itinerant spins and local ones enhances the quantum fluctuations around the classical long range antiferromagnetic order and finally destroy the ordered phase at the critical value ${J}_{c}$. Moreover, our results show that the onset of anisotropy in the $XY$ term of the itinerant interactions develops the antiferromagnetic order for $J<{J}_{c}$. This is in agreement with the qualitative feature which we expect from the symmetry of the anisotropic $XY$ interaction. We have justified our results by the numerical Lanczos method where the structure factor at the antiferromagnetic wave vector diverges as the size of system goes to infinity.

arXiv:0712.3914•Physical Review B•Jan 18, 2008•12 citations

Quantum phase transitions in the Kondo-necklace model

S. Hematian, M. Rahimi Movassagh, A. Langari +2 more

The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the perturbative continuous unitary transformations approach to calculate the energy gap and spin-spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green's function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.

•Dec 25, 2011•0 citations

Gap formation and phase transition of the anisotropic Kondo necklace model: Density matrix renormalization group analysis

Juan José Mendoza-Arenas, R. Franco, Jereson Silva-Valencia

We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter $\ensuremath{\eta}$ in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with $\ensuremath{\eta}$, but when $\ensuremath{\eta}$ approaches zero, they drop abruptly.

Physical Review B•Jan 8, 2010•11 citations

Planar and local anisotropies in the Kondo necklace model

Juan José Mendoza-Arenas, R. Franco, Jereson Silva-Valencia

Abstract Using the density matrix renormalization group method, we study the one‐dimensional Kondo necklace model including two anisotropies: η in the XY interaction of the conduction chain, and Δ in the local Kondo coupling between localized and conduction spins. For different values of the anisotropies, we calculate the energy gap and estimate the quantum critical points in which a phase transition from antiferromagnetic to spin liquid states takes place, assuming a Kosterlitz–Thouless‐like behavior. For the case $\eta = 0$ , the system remains in a spin liquid state for the different Δ considered, but when $\eta \ne 0$ , Δ markedly affects the location of the critical points. We also calculate correlation functions for a specific case, in order to support our gap results.

physica status solidi (b)•Feb 8, 2010•3 citations

Thermodynamic quantum critical behavior of the Kondo necklace model

Daniel Reyes, M. A. Contínentino

We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions $d$ using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in $d\ensuremath{\geqslant}3$, there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In two dimensions, long-range magnetic order occurs only at $T=0$. The line of N\'eel transitions for $d>2$ varies with the distance to the quantum critical point QCP $\ensuremath{\mid}g\ensuremath{\mid}$ as ${T}_{N}\ensuremath{\propto}{\ensuremath{\mid}g\ensuremath{\mid}}^{\ensuremath{\psi}}$, where the shift exponent $\ensuremath{\psi}=1∕(d\ensuremath{-}1)$. In the paramagnetic side of the phase diagram, the spin gap behaves as $\ensuremath{\Delta}\ensuremath{\approx}\sqrt{\ensuremath{\mid}g\ensuremath{\mid}}$ for $d\ensuremath{\geqslant}3$, consistent with the value $z=1$ found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for ${k}_{B}T⪢\ensuremath{\Delta}$ and along the non-Fermi-liquid trajectory. For ${k}_{B}T⪡\ensuremath{\Delta}$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.

arXiv:0706.1384•Physical Review B•Aug 15, 2007•26 citations
We have studied the effect of anisotropies on the quantum phase transition of the Kondo necklace model in dimensions D=1D=1D=1, 2, and 3. Both the anisotropy \ensuremathδ\ensuremath{\delta}\ensuremathδ of the intersite interaction term and anisotropy \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ of the on-site Kondo interaction have been included. We use a bond operator method with constraints implemented in mean-field approximation. Starting from the paramagnetic phase we determine the critical ratio (t∕J)c{(t∕J)}_{c}(t∕J)c​ of the quantum critical point and associated scaling exponents of the Kondo-singlet gap. We show that in the case of easy-axis type anisotropy \ensuremathδ>1\ensuremath{\delta}>1\ensuremathδ>1 a qualitatively different behavior in comparison to the conventional Kondo necklace model with (\ensuremathδ,\ensuremathΔ)=(0,1)(\ensuremath{\delta},\ensuremath{\Delta})=(0,1)(\ensuremathδ,\ensuremathΔ)=(0,1) appears. We have also obtained the antiferromagnetic order parameter in the long range ordered phase for t>tct>{t}_{c}t>tc​.
We have studied the quantum phase transition between the antiferromagnetic and spin liquid phases for the two-dimensional anisotropic Kondo necklace model. The bond operator formalism has been implemented to transform the spin Hamiltonian to a bosonic one. We have used the Green's function approach including a hard core repulsion to find the low energy excitation spectrum of the model. The bosonic excitations become gapless at the quantum critical point where the phase transition from the Kondo singlet state to long range antiferromagnetic order takes place. We have studied the effect of both intersite $(\ensuremath{\delta})$ and local $(\ensuremath{\Delta})$ anisotropies on the critical point and on the critical exponent of the excitation gap in the paramagnetic phase. We have also compared our results with previous bond operator mean field calculations.
The one-dimensional anisotropic Kondo-necklace model has been studied by several methods. It is shown that a mean field approach fails to gain the correct phase diagram for the Ising-type anisotropy. We then applied the spin wave theory which is justified for the anisotropic case. We have derived the phase diagram between the antiferromagnetic long range order and the Kondo singlet phases. We have found that the exchange interaction (J)(J)(J) between the itinerant spins and local ones enhances the quantum fluctuations around the classical long range antiferromagnetic order and finally destroy the ordered phase at the critical value Jc{J}_{c}Jc​. Moreover, our results show that the onset of anisotropy in the XYXYXY term of the itinerant interactions develops the antiferromagnetic order for J<JcJ<{J}_{c}J<Jc​. This is in agreement with the qualitative feature which we expect from the symmetry of the anisotropic XYXYXY interaction. We have justified our results by the numerical Lanczos method where the structure factor at the antiferromagnetic wave vector diverges as the size of system goes to infinity.
The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the perturbative continuous unitary transformations approach to calculate the energy gap and spin-spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green's function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.
We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter $\ensuremath{\eta}$ in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with $\ensuremath{\eta}$, but when $\ensuremath{\eta}$ approaches zero, they drop abruptly.
Abstract Using the density matrix renormalization group method, we study the one‐dimensional Kondo necklace model including two anisotropies: η in the XY interaction of the conduction chain, and Δ in the local Kondo coupling between localized and conduction spins. For different values of the anisotropies, we calculate the energy gap and estimate the quantum critical points in which a phase transition from antiferromagnetic to spin liquid states takes place, assuming a Kosterlitz–Thouless‐like behavior. For the case η=0\eta = 0η=0 , the system remains in a spin liquid state for the different Δ considered, but when η≠0\eta \ne 0η=0 , Δ markedly affects the location of the critical points. We also calculate correlation functions for a specific case, in order to support our gap results.
We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions ddd using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in $d\ensuremath{\geqslant}3$, there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In two dimensions, long-range magnetic order occurs only at T=0T=0T=0. The line of N\'eel transitions for d>2d>2d>2 varies with the distance to the quantum critical point QCP $\ensuremath{\mid}g\ensuremath{\mid}$ as ${T}_{N}\ensuremath{\propto}{\ensuremath{\mid}g\ensuremath{\mid}}^{\ensuremath{\psi}}$, where the shift exponent $\ensuremath{\psi}=1∕(d\ensuremath{-}1)$. In the paramagnetic side of the phase diagram, the spin gap behaves as $\ensuremath{\Delta}\ensuremath{\approx}\sqrt{\ensuremath{\mid}g\ensuremath{\mid}}$ for $d\ensuremath{\geqslant}3$, consistent with the value z=1z=1z=1 found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for ${k}_{B}T⪢\ensuremath{\Delta}$ and along the non-Fermi-liquid trajectory. For ${k}_{B}T⪡\ensuremath{\Delta}$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.