Quantum phase transitions in the Kondo-necklace model

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.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.

arXiv:1112.5783Journal of Physics Condensed MatterMar 27, 20152 citations

Nader Ghassemi, Shayan Hemmatiyan, M. Rahimi Movassagh +3 more

Kondo-necklace model can describe the magnetic low-energy limit of strongly correlated heavy fermion materials. There exists multiple energy scales in this model, each of which indicates a phase. Here, we study quantum phase transitions between these different phases, and show the effect of anisotropies in terms of quantum information properties and the vanishing of energy gap. We employ the perturbative unitary transformations to calculate the energy gap and spin-spin correlations for the model in spatial dimensions d = 1, 2, and 3 as well as for the spin ladders. In particular, we show that the method, although being perturbative, can detect the phase transition point by imposing the spontanous symmetry breaking, in good agreement with numerical and Green’s function methods . We also use concurrence, a bipartite entanglement measure, to probe the criticality of the model. This is based on finding points or regions in which the derivative of concurrence shows non-analyticity. This concurrence is also able to detect critical points in indicative of that the quantum correlations in this model are basically bipartite. Moreover, we discuss the crossover from the 1to 2-dimensional model via the ladder structures.Kondo-necklace model can describe the magnetic low-energy limit of strongly correlated heavy fermion materials. There exists multiple energy scales in this model, each of which indicates a phase. Here, we study quantum phase transitions between these different phases, and show the effect of anisotropies in terms of quantum information properties and the vanishing of energy gap. We employ the perturbative unitary transformations to calculate the energy gap and spin-spin correlations for the model in spatial dimensions d = 1, 2, and 3 as well as for the spin ladders. In particular, we show that the method, although being perturbative, can detect the phase transition point by imposing the spontanous symmetry breaking, in good agreement with numerical and Green’s function methods . We also use concurrence, a bipartite entanglement measure, to probe the criticality of the model. This is based on finding points or regions in which the derivative of concurrence shows non-analyticity. This concurrence is also able to detect critical points in indicative of that the quantum correlations in this model are basically bipartite. Moreover, we discuss the crossover from the 1to 2-dimensional model via the ladder structures.

Bulletin of the American Physical SocietyMar 2, 20151 citation

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

A. Langari, Peter Thalmeier

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 $t>{t}_{c}$ .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 $t>{t}_{c}$.

arXiv:cond-mat/0605191Physical Review BJul 31, 200622 citations

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.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:0802.0736Physical Review BMar 28, 200822 citations

ENTANGLEMENT IN THE ANISOTROPIC KONDO NECKLACE MODEL

Juan José Mendoza-Arenas, Roberto Franco, Jereson Silva-Valencia

We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.

International Journal of Modern Physics BDec 20, 20101 citation

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.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:0712.3914Physical Review BJan 18, 200812 citations

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}

(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.