The Ising-like anisotropy parameter $δ$ in the Kondo necklace model is analyzed using the bond-operator method at zero and finite temperatures 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. At zero temperature and in the paramagnetic side of the phase diagram, we determine the spin gap exponent $νz\approx0.5$ in three dimensions and anisotropy between $0\leqδ\leq1$, a result consistent with the dynamic exponent $z=1$ for the Gaussian character of the bond-operator treatment. At low but finite temperatures, in the antiferromagnetic phase, the line of Neel transitions is calculated for $δ\ll1$ and $δ\approx1$. For $d>2$ it is only re-normalized by the anisotropy parameter and varies with the distance to the quantum critical point QCP $|g|$ as, $T_N \propto |g|^ψ$ where the shift exponent $ψ=1/(d-1)$. Nevertheless, in two dimensions, long range magnetic order occurs only at T=0 for any $δ$. In the paramagnetic phase, we find a power law temperature dependence on the specific heat at the \textit{quantum liquid trajectory} $J/t=(J/t)_{c}$, $T\to0$. It behaves as $C_{V}\propto T^{d}$ for $δ\leq 1$ and $δ\approx1$, in concordance with the scaling theory for $z=1$.
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 $δ$ of the inter-site interaction term and anisotropy $Δ$ 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 $δ>1$ a qualitatively new be…
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. We conclude that these transitions belong to Ising universality class being, therefore, second order transitions instead of infinite order as claimed before…
A simplified version of the symmetric Kondo lattice model, the Kondo necklace model, is studied by using a representation of impurity and conduction electron spins in terms of local Kondo singlet and triplet operators. Within a mean field theory, a spin gap always appears in the spin triplet excitation spectrum in 1D, leading to a Kondo spin liquid state for any finite values of coupling strength $t/J$ (with $t$ as hopping and $J$ as exchange); in 2D and 3D cubic lattices the spin gaps are found to vanish continuously around $(t/J)_c\approx 0.70$ and $(t/J)_c\approx 0.38$, respectively, where …
We investigate the ground state of the Kondo necklace model on geometrically-frustrated lattices by the variational Monte Carlo simulation. To explore the possibility of a partially-ordered phase, we employ an extension of the Yosida-type wave function as a variational state, which can describe a coexistence of spin-singlet formation due to the Kondo coupling and magnetic ordering by the Ruderman-Kittel-Kasuya-Yosida interaction. We show the benchmark of the numerical simulation to demonstrate the high precision brought by the optimization of a large number of variational parameters. We discus…
We analyze the effects of site-dilution disorder on the thermodynamic properties of the two-dimensional Kondo necklace using finite-temperature stochastic series expansion. Results will be discussed for the dependence on dilution concentration, temperature, and Kondo exchange-coupling strength of the uniform susceptibility, the staggered structure factor, and the Chakravarty-Halperin-Nelson ratio. Dilution is shown to induce effective free-spin clusters in the gapped phase of the clean system with a low-temperature Curie constant renormalized below 1/4. Furthermore, dilution is demonstrated to…
The anisotropic Kondo necklace model in 2D and 3D is treated as a genuine model for magnetic to Kondo singlet quantum phase transitions in the heavy fermion (HF) compounds. The variation of the quantum critical point (QCP) with anisotropy parameters has been investigated previously in the zero field case [1]. Here we extend the treatment to finite fields using a generalised bond operator representation including all triplet states. The variation of critical tc with external field H and the associated phase diagram is derived. The influence of anisotropies and the different g-factors for locali…
We have studied the quantum phase transition between the antiferromagnetic and spin liquid phase 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 i…
The interplay between Kondo screening, indirect magnetic interaction and geometrical frustration is studied in the two-dimensional Kondo-necklace model on the triangular lattice. Using infinite projected entangled pair states (iPEPS), we compute the ground state as a function of the antiferromagnetic local Kondo interaction $J_K$ and the Ising-type direct spin-spin interaction $I_z$ . As opposed to previous studies, we do not find partial Kondo screening (PKS) in the isotropic limit $I_z = 0$ but the same behavior as in the unfrustrated case, i.e. a direct phase transition between the paradigm…
We study a lattice realization of a Luttinger liquid interacting with a bath of quantum spins in terms of an antiferromagnetic S=1/2 Heisenberg chain, where each spin is also coupled to a σ=1/2 Kondo spin degree of freedom. This model describes the low-energy spin dynamics in quasi one dimensional materials, where the electronic spins of the magnetic ions interact with those of impurities, nuclei and possibly other spin species present in their environment. For large ferromagnetic and antiferromagnetic Kondo interaction J' there are two phases corresponding to an effective spin-1 Heisenberg ch…
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 $d\geq 3$ there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In 2-d, long range magnetic order occurs only at T=0. The line of Neel transitions for $d>2$ varies …
In this paper we investigate the magnetic properties of heavy fermions in the antiferromagnetic and dense Kondo phases in the framework of the Kondo necklace model. We use a mean field renormalization group approach to obtain a temperature versus Kondo coupling $(T-J)$ phase diagram for this model in qualitative agreement with Doniach's diagram, proposed on physical grounds. We further analyze the magnetically disordered phase using a two-sites approach. We calculate the correlation functions and the magnetic susceptibility that allow to identify the crossover between the spin-liquid and the l…
We analyse several thermodynamic properties of the two-dimensional Kondo necklace using finite-temperature stochastic series expansion. In agreement with previous zero-temperature findings the model is shown to exhibit a quantum critical point (QCP), separating an antiferromagnetic from a paramagnetic dimerized state at a critical Kondo exchange-coupling strength $J_{c}\approx 1.4$. We evaluate the temperature dependent uniform and staggered structure factors as well as the uniform and staggered susceptibilities and the local 'impurity' susceptibility close to the QCP as well as in the ordered…
We study single hole dynamics in the bilayer Heisenberg and Kondo Necklace models. Those models exhibit a magnetic order-disorder quantum phase transition as a function of the interlayer coupling J_perp. At strong coupling in the disordered phase, both models have a single-hole dispersion relation with band maximum at p = (π,π) and an effective mass at this p-point which scales as the hopping matrix element t. In the Kondo Necklace model, we show that the effective mass at p = (π,π) remains finite for all considered values of J_perp such that the strong coupling features of the dispersion rela…
The effect of strong disorder on the one-dimensional Kondo necklace model is studied using a perturbative real-space renormalization group approach which becomes asymptotically exact in the low energy limit. The phase diagram of the model presents a random quantum critical point separating two phases; the {\em random singlet phase} of a quantum disordered XY chain and the random Kondo phase. We also consider an anisotropic version of the model and show that it maps on the strongly disordered transverse Ising model. The present results provide a rigorous microscopic basis for non-Fermi liquid b…
The critical properties of the frustrated Kondo necklace model with a half saturation magnetization ($m=1/2$) have been studied by means of an exact-diagonalization method. It is shown from bosonization technique that the model can be effectively expressed as a quantum sine-Gordom model. Thus it may show three (dimer plateau, N{é}el plateau and Tomonaga-Luttinger liquid) phases due to competitions among the Ising anisotropy $Δ$, and the nearest- and next-nearest-neighbor exchange interactions $J_1$ and $J_2$. The boundary lines on the $Δ-J_2/J_1$ phase diagram separating the three phases are d…
Emergence of Kondo-assisted Néel order in a Kondo necklace model
Osaka Metropolitan University（大阪公立大学）；Innovative Quantum Material Center (IQMC), Osaka Metropolitan University（大阪公立大学创新量子材料中心）；Saitama Medical University（埼玉医科大学）；the University of Tokyo（东京大学）；Center for Advanced High Magnetic Field Science (AHMF), Graduate School of Science, Osaka University（大阪大学理学研究系先进高磁场科学研究中心）；National Defense Academy（防卫大学校）
Magnetization processes of frustrated Kondo necklace model are studied by means of a density matrix renormalization group (DMRG) method and an elementary band theory based on a bond-operator formalism. The DMRG calculations clearly show the cusp singularity in a low-magnetization region ($0<m<1/2$) besides that in a high-magnetization region ($1/2<m<1$) which is expected from previous studies on the magnetization curve of the Majumdar-Ghosh model. An appearance mechanism of the low-magnetization cusp is interpreted in terms of a double-well shape of a low-energy band arising from frustrations …
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 limi…
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 or…
We study possible topological features of Kondo spin liquid phase in terms of the one- and two-dimensional 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 fi…
Mapping reservoir-enhanced superconductivity to near-long-range magnetic order in the undoped 1D Anderson- and Kondo-lattices
Heriot-Watt University（赫瑞-瓦特大学）；University of Geneva（日内瓦大学）；Weizmann Institute of Science（魏茨曼科学研究所）；Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）
We report the thermodynamic, magnetic, and electronic transport properties of the new ternary intermetallic system (Ce,La)3Pt4In13. Ce3Pt4In13 orders antiferromagnetically at 0.95 K while the non-magnetic compound La3Pt4In13 is a conventional 3.3 K superconductor. Kondo lattice effects appear to limit the entropy associated with the Neel transition to (1/4)Rln2 as an electronic contribution to the specific heat of gamma = 1 J/mole-Ce K2 is observed at TN; roughly 35% of this gamma survives the ordering transition. Hall effect, thermoelectric power, and ambient-pressure resistivity measurements…
The magnetic correlations, local moments and the susceptibility in the correlated 2D Kondo lattice model at half filling are investigated. We calculate their systematic dependence on the control parameters J_K/t and U/t. An unbiased and reliable exact diagonalization (ED) approach for ground state properties as well as the finite temperature Lanczos method (FTLM) for specific heat and the uniform susceptibility are employed for small tiles on the square lattice. They lead to two major results: Firstly we show that the screened local moment exhibits non-monotonic behavior as a function of U for…
The unique linear density of state around the Dirac points for the honeycomb lattice brings much novel features in strongly correlated models. Here we study the ground-state phase diagram of the Kondo lattice model on the honeycomb lattice at half-filling by using an extended mean-field theory. By treating magnetic interaction and Kondo screening on an equal footing, it is found that besides a trivial discontinuous first-order quantum phase transition between well-defined Kondo insulator and antiferromagnetic insulating state, there can exist a wide coexistence region with both Kondo screening…
We consider a spin-1/2 ladder with a ferromagnetic rung coupling J_\perp and inequivalent chains. This model is obtained by a twist (θ) deformation of the ladder and interpolates between the isotropic ladder (θ=0) and the SU(2) ferromagnetic Kondo necklace model (θ=π). We show that the ground state in the (θ,J_\perp) plane has a finite string order parameter characterising the Haldane phase. Twisting the chain introduces a new energy scale, which we interpret in terms of a Suhl-Nakamura interaction. As a consequence we observe a crossover in the scaling of the spin gap at weak coupling from Δ/…
A zero temperature real space renormalization group (RG) approach is used to investigate the role of disorder near the quantum critical point (QCP) of a Kondo necklace (XY-KN) model. In the pure case this approach yields $J_{c}=0$ implying that any coupling $J \not = 0 $ between the local moments and the conduction electrons leads to a non-magnetic phase. We also consider an anisotropic version of the model ($X-KN$), for which there is a quantum phase transition at a finite value of the ratio between the coupling and the bandwidth, $(J/W)$. Disorder is introduced either in the on-site interact…
