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

Rezania, H.; Langari, A.; Thalmeier, Peter

doi:10.1103/physrevb.77.094438

Cited by 20 publications

(30 citation statements)

References 21 publications

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“…For λ < 1, we always obtained zero for the value of the concurrence. This implies concurrence is not sensitive to the quantum phase transition in 26 (GF), and zero gap through PCUT (G2 = 0 or G3 = 0). Kondo-necklace model in agreement with the results reported for one-dimensional Kondo-necklace model 41 .…”

Section: Summary and Discussionmentioning

confidence: 99%

“…This dependence instead implies dependence of the quantum critical point on ∆. For the two-dimensional model, the results from other methods such as the mean-filed 23 and Green's function 26 approaches are also available. Table II summarizes this ∆-dependence of the mentioned methods.…”

Section: A Energy Gapmentioning

confidence: 99%

“…However, the Z 2 -symmetric one-dimensional model exhibits a QPT to the antiferromagnetic order at λ c = 2.22 for the Ising interaction between τ -spins, i.e., η x = η y = 0 and η z = 1 25 . Unlike the one-dimensional model, both two-and threedimensional KN Hamiltonian with U (1) symmetry show a QPT from the disordered Kondo-singlet to the antiferromagnetic ordered phase 23,26,29 . The quantum critical point depends on the anisotropy parameters; however, λ c < 1 for both cases.…”

Section: Quantum Phase Transitionmentioning

confidence: 99%

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Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach

Hemmatiyan

Movassagh

Ghassemi

et al. 2015

J. Phys.: Condens. Matter

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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.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: A Energy Gapmentioning

confidence: 99%

Section: Quantum Phase Transitionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach

Hemmatiyan

Movassagh

Ghassemi

et al. 2015

J. Phys.: Condens. Matter

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show abstract

“…More explanations of the detailed calculations can be found in Ref. 15. Finally, the self-energy is expanded in the low energy limit which gives the single particle part of Green's function (G sp n ),…”

Section: Hard Core Representation Of Spin Hamiltonian and Bosonimentioning

confidence: 99%

“…The bilinear Hamiltonian is simply diagonalized by the unitary Bogoliuobov transformation to the new bosonic quasi particle operators α k and α † k , [15], which is given by…”

Section: Hard Core Representation Of Spin Hamiltonian and Bosonimentioning

confidence: 99%

Effect of anisotropy on the field-induced quantum critical properties of the three-dimensionals=12Heisenberg model

Rezania

Langari

2010

Phys. Rev. B

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The field induced quantum critical properties of the three dimensional spin-1/2 anisotropic antiferromagnetic Heisenberg model has been studied. We have investigated the quantum phase transition between the spiral order and field induced ferromagnetic order by means of Bose-Einstein condensation of magnons in terms of a bosonic representation. The effect of in-plane anisotropy on the critical properties has been studied via the bosonic model by Green's function approach. We have found an analytic expression for the gap exponent in addition to numerical results for the critical magnetic field in terms of anisotropy parameter. The in-plane anisotropy breaks the U(1) symmetry explicitly which changes the universal behavior by a drastic change on the gap exponent. Moreover, the critical magnetic field depends strongly on the in-plane anisotropies. The divergence of the transverse structure factor at the antiferromagnetic wave vector confirms the onset of the magnetic order which scales with the negative value of gap exponent as the magnetic field approaches the critical one. The transverse staggered magnetization as an order parameter vanishes with exponent β = 0.5 when the magnetic field reaches its critical value in low field region.

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Planar and local anisotropies in the Kondo necklace model

Mendoza‐Arenas¹,

Franco²,

Silva–Valencia³

2010

Physica Status Solidi (b)

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Using the density matrix renormalization group method, we study the one-dimensional Kondo necklace model including two anisotropies: h in the XY interaction of the conduction chain, and D 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-Thoulesslike behavior. For the case h ¼ 0, the system remains in a spin liquid state for the different D considered, but when h 6 ¼ 0, D markedly affects the location of the critical points. We also calculate correlation functions for a specific case, in order to support our gap results.

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

Cited by 20 publications

References 21 publications

Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach

Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach

Effect of anisotropy on the field-induced quantum critical properties of the three-dimensionals=12Heisenberg model

Planar and local anisotropies in the Kondo necklace model

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