Analysis of the Antiferromagnetic Phase Transitions of the 2D Kondo Lattice (original) (raw)
Related papers
2001
We present a detailed numerical study of ground state and finite temperature spin and charge dynamics of the two-dimensional Kondo lattice model with hopping t and exchange J. Our numerical results stem from auxiliary field quantum Monte Carlo simulations formulated in such a way that the sign problem is absent at half-band filling thus allowing us to reach lattice sizes up to 12 × 12. At T = 0 and antiferromagnetic couplings, J > 0, the competition between the RKKY interaction and Kondo effect triggers a quantum phase transition between antiferromagnetically ordered and magnetically disordered insulators: Jc/t = 1.45 ± 0.05. At J < 0 the system remains an antiferromagnetically ordered insulator and irrespective of the sign of J, the quasiparticle gap scales as |J|. The dynamical spin structure factor, S( q, ω), evolves smoothly from its strong coupling form with spin gap at q = (π, π) to a spin wave form. For J > 0, the single particle spectral function, A( k, ω), shows a dispersion relation following that of hybridized bands as obtained in the non-interacting periodic Anderson model. In the ordered phase this feature is supplemented by shadows thus allowing an interpretation in terms of coexistence of Kondo screening and magnetic ordering. In contrast, at J < 0 the single particle dispersion relation follows that of non-interacting electrons in a staggered external magnetic field. At finite temperatures spin, TS, and charge, TC , scales are defined by locating the maximum in the charge and spin uniform susceptibilities. For weak to intermediate couplings, TS marks the onset of antiferromagnetic fluctuations -as observed by a growth of the staggered spin susceptibility-and follows a J 2 law. At strong couplings TS scales as J. On the other hand TC scales as J both in the weak and strong coupling regime. At and slightly below TC we observe i) the onset of screening of the magnetic impurities, ii) a rise in the resistivity as a function of decreasing temperature, iii) a dip in the integrated density of states at the Fermi energy and finally iv) the occurrence of hybridized bands in A( k, ω). It is shown that in the weak coupling limit, the charge gap of order J is formed only at TS and is hence of magnetic origin. The specific heat shows a two peak structure. The low temperature peak follows TS and is hence of magnetic origin. Our results are compared to various mean-field theories.
Nonlinear Sigma Model Analysis of the AFM Phase Transition of the Kondo Lattice
2008
We have studied the antiferromagnetic quantum phase transition of a 2D Kondo-Heisenberg square lattice using the non-linear sigma model. A renormalization group analysis of the competing Kondo -- RKKY interaction was carried out to 1-loop order in the epsilon\epsilonepsilon expansion, and a new quantum critical point is found, dominated by Kondo fluctuations. In addition, the spin-wave velocity scales logarithmically near the new QCP, i.e breakdown of hydrodynamic behavior. The results allow us to propose a new phase diagram near the AFM fixed point of this 2D Kondo lattice model.
Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators
Journal of Low Temperature Physics, 2010
We discuss the general theoretical arguments advanced earlier for the T = 0 global phase diagram of antiferromagnetic Kondo lattice systems, distinguishing between the established and the conjectured. In addition to the wellknown phase of a paramagnetic metal with a "large" Fermi surface (P L), there is also an antiferromagnetic phase with a "small" Fermi surface (AF S). We provide the details of the derivation of a quantum non-linear sigma-model (QNLσ M) representation of the Kondo lattice Hamiltonian, which leads to an effective field theory containing both low-energy fermions in the vicinity of a Fermi surface and low-energy bosons near zero momentum. An asymptotically exact analysis of this effective field theory is made possible through the development of a renormalization group procedure for mixed fermion-boson systems. Considerations on how to connect the AF S and P L phases lead to a global phase diagram, which not only puts into perspective the theory of local quantum criticality for antiferromagnetic heavy fermion metals, but also provides the basis to understand the surprising recent experiments in chemically-doped as well as pressurized YbRh 2 Si 2. We point out that the AF S phase still occurs for the case of an equal number of spin-1/2 local moments and conduction electrons. This observation raises the prospect for a global phase diagram of heavy fermion systems in the Kondo-insulator regime. Finally, we discuss the connection between the Kondo breakdown physics discussed
Physical Review Letters
Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale TFL is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spinorbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, TFL becomes arbitrarily small close to two new quantum critical points (QCPs) which we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω −1/5), orbital (ω 1/5) and spin-orbital (ω 1) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.
Physical Review B, 1997
Formation of magnetically ordered state in the Kondo lattices is treated within the degenerate s − f exchange and Coqblin-Schrieffer models. The Kondo renormalizations of the effective coupling parameter, magnetic moment and spin excitation frequencies are calculated within perturbation theory. The results of one-loop scaling consideration of the magnetic state in Kondo lattices are analyzed. The dependence of the critical values of the bare model parameters on the type of the magnetic phase and space dimensionality is investigated. Renormalization of the effective Kondo temperature by the interatomic exchange interactions is calculated. An important role of the character of spin dynamics (existence of well-defined magnon excitations, presence of magnetic anisotropy etc.) is demonstrated. The regime of strongly suppressed magnetic moments, which corresponds to magnetic heavy-fermion system, may occur in a rather narrow parameter region only. At the same time, in the magnetically ordered phases the renormalized Kondo temperature depends weakly on the bare coupling parameter in some interval. The critical behavior, corresponding to the magnetic transition with changing the bare s − f coupling parameter, is investigated. In the vicinity of the strong coupling regime, the spectrum of the Bose excitations becomes softened. Thus on the borderline of magnetic instability the Fermiliquid picture is violated in some temerature interval due to scattering of electrons by these bosons. This may explain the fact that a non-Fermi-liquid behavior often takes place in the heavy-fermion systems near the onset of magnetic ordering.
Small Fermi surface in the one-dimensional Kondo lattice model
Physical Review B, 2002
We study the one-dimensional Kondo lattice model through the density-matrix renormalization group. Our results for the spin-correlation function indicate the presence of a small Fermi surface in large portions of the phase diagram, in contrast to some previous studies that used the same technique. We argue that the discrepancy is due to the open boundary conditions, which introduce strong charge perturbations that strongly affect the spin Friedel oscillations.
The non-Fermi-liquid behavior in magnetic Kondo lattices induced by peculiarities of spin dynamics
Physics Letters A, 2000
A scaling consideration of the Kondo lattices is performed with account of singularities in the spin excitation spectral Ž . function. It is shown that a non-Fermi-liquid NFL behaviour occurs naturally for complicated magnetic structures with several magnon branches. This may explain the fact that a NFL behaviour often takes place in the heavy-fermion systems with peculiar spin dynamics. The mechanisms proposed lead to some predictions about behaviour of specific heat, resistivity, magnetic susceptibility and anisotropy parameter, which can be verified experimentally. q 2000 Published by Elsevier Science B.V. All rights reserved. PACS: 75.30.Mb; 71.28 0375-9601r00r$ -see front matter q 2000 Published by Elsevier Science B.V. All rights reserved.
Undressing the Kondo Effect near the Antiferromagnetic Quantum Critical Point
Physical Review Letters, 2005
The problem of a spin-1=2 magnetic impurity near an antiferromagnetic transition of the host lattice is shown to transform to a multichannel problem. A variety of fixed points is discovered asymptotically near the antiferromagnetic critical point. Among these is a new variety of stable fixed point of a multichannel Kondo problem which does not require channel isotropy. At this point Kondo screening disappears but coupling to spin fluctuations remains. In addition to its intrinsic interest, the problem is an essential ingredient in the problem of quantum critical points in heavy fermions.
Physics Subject Headings (PhySH)
In this lecture, we review the experimental situation of heavy Fermions with emphasis on the existence of a quantum phase transition (QPT) and related non-Fermi liquid (NFL) effects. We overview the Kondo lattice model (KLM) which is believed to describe the physics of those systems. After recalling the existing theories based on large-N expansion and various N=2 schemes, we present two alternative approaches: (i) a spin fluctuation-Kondo functional integral approach treating the spin-fluctuation and Kondo effects on an equal footing, and (ii) a supersymmetric theory enlarging the usual fermionic representation of the spin into a mixed fermionic-bosonic representation in order to describe the spin degrees of freedom as well as the Fermi-liquid type excitations. This kind of approaches may open up new prospects for the description of the critical phenomena associated to the quantum phase transition in Heavy-Fermion systems.