Green’s function approach to the thermodynamic properties of the anisotropic Kondo necklace model

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

doi:10.1103/physrevb.79.094401

Cited by 14 publications

(4 citation statements)

References 28 publications

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“…As a result, the interplaquette interactions hybridize the ground state of a single plaquette with the corresponding excited eigenstates. In order to take into account the effect of inter-plaquette interactions, we implement a bosonization formalism 33 similar to what has been introduced as bond-operator representation of spin systems [34][35][36][37][38][39] . A boson is associated to each eigenstate |u of a single-plaquette Hamiltonian such that the eigenstate is created by the corresponding boson creation operator b † I,u acting on the vacuum,…”

Section: B Interaction Between Plaquettes: a Bosonic Representationmentioning

confidence: 99%

Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

Sadrzadeh

Langari

2015

Eur. Phys. J. B

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We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the antiferromagnetic J1 − J2 Ising model on the checkerboard lattice, the two dimensional version of the pyrochlore lattice. The zero-temperature phase diagram of the model has been obtained by employing a plaquette operator approach (POA). The plaquette operator formalism bosonizes the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered solid (RPS) state, which breaks lattice translational symmetry, in addition to a unique collinear phase for J2 > J1. The bosonic excitation gap vanishes at the critical points to the Néel (J2 < J1) and collinear (J2 > J1) ordered phases, which defines the critical phase boundaries. At the homogeneous coupling (J2 = J1) and its close neighborhood, the (canted) RPS state, established from an-harmonic fluctuations, lasts for low fields, Γ/J1 0.3, which is followed by a transition to the quantum paramagnet (polarized) phase at high fields. The transition from RPS state to the Néel phase is either a deconfined quantum phase transition or a first order one, however a continuous transition occurs between RPS and collinear phases.

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Section: B Interaction Between Plaquettes: a Bosonic Representationmentioning

confidence: 99%

Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

Sadrzadeh

Langari

2015

Eur. Phys. J. B

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“…Now, if we extend 1D Kondo necklace model to higher space dimension, besides the Kondo spin liquid phase, the usual antiferromagnetic insulating state appears (We only consider bipartite lattice as square and honeycomb lattices). 24,28,30,31 It has been suggested that there may exist a second quantum phase transition between these two. 24,30 Based on previous discussion, we may considered the 2D Kondo necklace model as a bilayer antiferromagnet with antiferromagnetic inter-layer coupling.…”

Section: Kondo Spin Liquid In Higher Spatial Dimension and Possible R...mentioning

confidence: 99%

“…1 The Kondo necklace model is widely studied in many analytical and numerical methods, and most of them focus on the one-dimensional (1D) case. [21][22][23][24][25][26][27][28][29][30][31][32][33][34] It is now believed that in 1D, the system is always gapped and the ground-state is in the Kondo spin singlet phase (also named Kondo spin liquid phase). The issues for higher dimension are still open.…”

Section: Introductionmentioning

confidence: 99%

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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“…On the other hand, at higher dimensions, it is found that the model presents a quantum critical point (QCP) where the nonmagnetic gapped phase goes to zero and at the same time appears a magnetic gapless phase [13][14][15][16]. Then, the KNM was used for studying the effect of magnetic field [17], thermal and magnetic entanglement [18], dimensional crossover [19,20], and anisotropy [21][22][23] in the heavy fermion compounds. Disorder was also considered in the one dimensional KNM, and all seems to indicate that it is an essential ingredient in the study of the heavy fermions materials [24,26].…”

Section: Introductionmentioning

confidence: 98%

Quantum critical behavior of the Kondo necklace model with aperiodic exchange modulation

Reyes

Landauro

2010

Journal of Magnetism and Magnetic Materials

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a b s t r a c tThe low energy behavior of the Kondo necklace model with an aperiodic exchange modulation is studied using a representation for the localized and conduction electron spins, in terms of local Kondo singlet and triplet operators at zero and finite temperature for arbitrary d dimensions. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. We determined the dependence between the chemical aperiodic exchange modulation and the spin gap in 1d, 2d and 3d, at zero temperature and in the paramagnetic side of the phase diagram. On the other hand, at low but finite temperatures, the line of Né el transitions in the antiferromagnetic phase is calculated in function of the aperiodic exchange modulation.

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Green’s function approach to the thermodynamic properties of the anisotropic Kondo necklace model

Cited by 14 publications

References 28 publications

Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

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

Quantum critical behavior of the Kondo necklace model with aperiodic exchange modulation

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