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

Mendoza‐Arenas, J. J.; Franco, R.; Silva–Valencia, J.

doi:10.1103/physrevb.81.035103

Cited by 9 publications

(9 citation statements)

References 23 publications

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“…For comparison we also show in this figure the results obtained in Refs. [8,9,10]. As it can been seen, our calculations indicate that the system exhibits two phases for any finite value of anisotropy.…”

Section: Resultssupporting

confidence: 67%

“…The model is suitable to describe heavy fermion systems and emphasizes magnetic degrees of freedom neglecting The critical line separates the antiferromagnetic phase (below each line) from the non-magnetic ground state. For comparison we also show the results obtained by DMRG method [10], Lanczos calculation [9], and RSRG approach [8].…”

Section: Discussionmentioning

confidence: 99%

“…The Ising like anisotropy parameter (δ) varies from zero to one. The zero temperature phase diagram of this model in the (δ,K) plane, with K = J/W , has been studied by different methods as renormalization group [8], Lanczos [9], and DMRG [10]. The main results found in the literature can be summarized as follows.…”

Section: Introductionmentioning

confidence: 99%

“…[8], or if it is present for any value of anisotropy, as reported in Refs. [9,10]. Other important point of discussion is the class of universality of the ordered-disordered transition.…”

Section: Introductionmentioning

confidence: 99%

“…RG calculation indicates it is a second order phase transition but the authors of Ref. [10] proposed it is of Kosterlitz-Thouless type.…”

Section: Introductionmentioning

confidence: 99%

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Study of the 1D anisotropic Kondo necklace model at criticality via an entanglement entropy estimator

Saguia

2013

Physics Letters A

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We use an estimator of quantum criticality based on the entanglement entropy to discuss the ground state properties of the 1D anisotropic Kondo necklace model. We found that the T = 0 phase diagram of the model is described by a critical line separating an antiferromagnetic phase from a Kondo singlet state. Moreover we calculate the conformal anomaly on the critical line and obtained that c tends to 0.5 as the thermodynamic limit is reached. Hence we conclude that these transitions belong to Ising universality class being, therefore, second order transitions instead of infinite order as claimed before. * Email address: amen@if.uff.br (A. Saguia) Block of l' = 4 spins size J S σ σ J W W S J S J J J W W W S S 5 6

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Section: Resultssupporting

confidence: 67%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…[8], or if it is present for any value of anisotropy, as reported in Refs. [9,10]. Other important point of discussion is the class of universality of the ordered-disordered transition.…”

Section: Introductionmentioning

confidence: 99%

“…RG calculation indicates it is a second order phase transition but the authors of Ref. [10] proposed it is of Kosterlitz-Thouless type.…”

Section: Introductionmentioning

confidence: 99%

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Study of the 1D anisotropic Kondo necklace model at criticality via an entanglement entropy estimator

Saguia

2013

Physics Letters A

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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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Kondo spin liquid in the Kondo necklace model: Classical disordered phase versus symmetry-protected topological state

Zhong

Wang

et al. 2014

Physica B: Condensed Matter

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We study possible topological features of Kondo spin liquid phase in terms of the one-and twodimensional Kondo necklace models within the frame work of quantum O(N) non-liner sigma model (NLSM). In the one-dimensional case, it is found that the bulk properties of the Kodno spin liquid phase are similar to the well-known Haldane phase at strong coupling fixed point. The difference between them mainly comes from their boundaries due to the effect of the topological term. In the two-dimensional case, the system can be mapped onto an O(4)-like NLSM with some O(3) anisotropy. Interestingly, we find that if hedgehog-like point defects are included together with the restoration of the full O(4) symmetry, our model is identical to a kind of SU(2) symmetryprotected topological (SPT) state. Additionally, if the system has the O(5) symmetry instead, the effective NLSM with Wess-Zumino-Witten term is just a description of the surface modes of a threedimensional SPT state, though such O(5) NLSM could not be a proper description of Kondo spin liquid phase due to its gaplessness. We expect that the discussions might provide useful threads to identify certain microscopic bilayer antiferromagnet models (and related materials), which can support the desirable SPT states.

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

Cited by 9 publications

References 23 publications

Study of the 1D anisotropic Kondo necklace model at criticality via an entanglement entropy estimator

Study of the 1D anisotropic Kondo necklace model at criticality via an entanglement entropy estimator

Planar and local anisotropies in the Kondo necklace model

Kondo spin liquid in the Kondo necklace model: Classical disordered phase versus symmetry-protected topological state

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