Nonlinear Sigma Model Analysis of the AFM Phase Transition of the Kondo Lattice (original) (raw)
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Analysis of the Antiferromagnetic Phase Transitions of the 2D Kondo Lattice
Physical Review Letters, 2009
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 ǫ 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.
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.
The fate of Kondo resonances in certain Kondo lattices: a ‘poor woman’s’ scaling analysis
Journal of Physics: Condensed Matter, 2005
We present an effective field theory for the Kondo lattice, which can exhibit, in a certain range of parameters, a non Fermi liquid paramagnetic phase at the brink of a zero temperature Anti Ferromagnetic (AF) transition. The model is derived in a natural way from the bosonic Kondo-Heisenberg model, in which the Kondo resonances are seen as true (but damped) Grassmann fields in the field theory sense. One loop Renormalization Group (RG) treatment of this model gives a phase diagram for the Kondo lattice as a function of JK where, for JK < Jc the system shows AF order, for JK > J1 one has the heavy electron phase and for Jc < JK < J1 the formation of the Kondo singlets is incomplete, leading to the breakdown of the Landau Fermi liquid theory.
The Kondo Lattice Model in Infinite Dimensions: II. Static Susceptibilities and Phase Diagram
Journal of the Physical Society of Japan, 2009
Magnetic and charge susceptibilities in the Kondo lattice are derived by the continuous-time quantum Monte Carlo (CT-QMC) method combined with the dynamical mean-field theory. For a weak exchange coupling J and near half filling of the conduction band, antiferromagnetic transition occurs as signalled by divergence of the staggered magnetic susceptibility with lowering temperature. With increasing J, the Kondo effect suppresses the divergence, and the critical value of J agrees well with Doniach's estimate which considers the RKKY interaction as competing with the Kondo effect. For low density of conduction electrons, a ferromagnetic ordering is observed where Doniach's estimate does not work. Around quarter filling, a chargedensity-wave (CDW) transition is found. The CDW is interpreted from the strong-coupling limit in terms of effective repulsion between Kondo singlets.
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.
Effects of the Berry Phase and Instantons in One-Dimensional Kondo-Heisenberg Model
Physical Review Letters, 2011
Motivated by the recent considerations of the global phase diagram of antiferromagnetic heavy fermion metals, we study the Kondo effect from the perspective of the nonlinear sigma model in the one dimensional Kondo-Heisenberg model. We focus on the effects of the instanton configurations of the sigma-model field and the associated Berry phase. With the guidance provided by the considerations based on the bosonization methods, we demonstrate that the Kondo singlet formation is accompanied by an emergent Berry phase. This Berry phase also captures the competition between the Kondo singlet formation and the spin Peierls correlations. Related effects are likely to be realized in Kondo lattice systems of higher dimensions.
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.
Kondo Destruction and Quantum Criticality in Kondo Lattice Systems
Journal of the Physical Society of Japan, 2014
Considerable efforts have been made in recent years to theoretically understand quantum phase transitions in Kondo lattice systems. A particular focus is on Kondo destruction, which leads to quantum criticality that goes beyond the Landau framework of order-parameter fluctuations. This unconventional quantum criticality has provided an understanding of the unusual dynamical scaling observed experimentally. It also predicted a sudden jump of the Fermi surface and an extra (Kondo destruction) energy scale, both of which have been verified by systematic experiments. Considerations of Kondo destruction have in addition yielded a global phase diagram, which has motivated the current interest in heavy fermion materials with variable dimensionality or geometrical frustration. Here we summarize these developments, and discuss some of the ongoing work and open issues. We also consider the implications of these results for superconductivity. Finally, we address the effect of spin-orbit coupling on the global phase diagram, suggest that SmB 6 under pressure may display unconventional superconductivity in the transition regime between a Kondo insulator phase and an antiferroamgnetic metal phase, and argue that the interfaces of heavy-fermion heterostructures will provide a fertile setting to explore topological properties of both Kondo insulators and heavyfermion superconductors.