Kondo lattice model (original) (raw)

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.

Theory of the non-Fermi-liquid transition point in the two-impurity Kondo model

Physical review. B, Condensed matter, 1993

We present an explicit solution of the problem of two coupled spin-impurities, interacting with a band of conduction electrons. We obtain an exact e6'ective bosonized Hamiltonian, which is then treated by two different methods (low-energy theory and mean-field approach). Scale invariance is explicitly shown at the quantum critical point. The staggered susceptibility behaves like ln(T&/T) at low T, whereas the magnetic susceptibility and (S,. sz) are well behaved at the transition. The divergence of C (T) /T when approaching the transition point is also studied. The non-Fermi-liquid (actually marginal-Fermi-liquid) critical point is shown to arise because of the existence of anomalous correlations, which lead to degeneracies between bosonic and fermionic states of the system. The methods developed in this paper are of interest for studying more physically relevant models, for instance, for high-T, cuprates.

Quantum phase transitions and thermodynamics of the power-law Kondo model

We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, ~|w|^r, with exponent -1<r<0. Using the analytical understanding of several xed points, based partially on powerful mappings between models with bath exponents r and (-r), combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases, and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum eld theories for all critical xed points of the problem, which are fermionic in nature and allow for a perturbative renormalization- group treatment.

Frustration and the Kondo Effect in Heavy Fermion Materials

Journal of Low Temperature Physics, 2010

The observation of a separation between the antiferromagnetic phase boundary and the small-large Fermi surface transition in recent experiments has led to the proposal that frustration is an important additional tuning parameter in the Kondo lattice model of heavy fermion materials. The introduction of a Kondo (K) and a frustration (Q) axis into the phase diagram permits us to discuss the physics of heavy fermion materials in a broader perspective. The current experimental situation is analysed in the context of this combined "QK" phase diagram. We discuss various theoretical models for the frustrated Kondo lattice, using general arguments to characterize the nature of the f-electron localization transition that occurs between the spin liquid and heavy Fermi liquid ground-states. We concentrate in particular on the Shastry-Sutherland Kondo lattice model, for which we establish the qualitative phase diagram using strong coupling arguments and the large-N expansion. The paper closes with some brief remarks on promising future theoretical directions.

Interplay of Kondo effect and magnetic correlation in heavy fermion systems

Indian Journal of Physics, 2012

We report here the theory of the heavy fermion systems by a model Hamiltonian consisting of the usual Kondo lattice including an antiferromagnetic exchange interaction between the nearest neighbour localized spins. The Hamiltonian is treated in a mean-field approximation that introduces two mean-field parameters: the first one is associated with the magnetic correlation between the localized spins and the second one is related to the local Kondo effect. The short range magnetic correlations and the Kondo parameters are obtained by minimizing the total energy of the system and are solved self-consistently taking into account of the total number of electrons. The density of states for c-and f-electrons is studied for the different model parameters of the system.

Two-channel pseudogap Kondo and Anderson models: Quantum phase transitions and non-Fermi liquids

Physical Review B, 2011

We discuss the two-channel Kondo problem with a pseudogap density of states, ρ(ω) ∝ |ω| r , of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi liquid behavior of the metallic r = 0 case, is replaced by a stable particle-hole symmetric intermediate-coupling fixed point for 0 < r < rmax ≈ 0.23. For r > rmax, this non-Fermi liquid phase disappears, and instead a critical fixed point with an emergent spin-channel symmetry appears, controlling the quantum phase transition between two phases with stable spin and channel moments, respectively. We propose lowenergy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ epsilon expansion techniques to calculate critical properties near the critical dimensions r = 0 and r = 1, the latter being potentially relevant for two-channel Kondo impurities in neutral graphene. We find the analytical results to be in excellent agreement with those obtained from applying Wilson's numerical renormalization group technique.

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.

Fermi-liquid regime of the mesoscopic Kondo problem

We consider the low temperature regime of the mesoscopic Kondo problem, and in particular the relevance of a Fermi-liquid description of this regime. Using two complementary approaches -a mean field slave fermion approximation on the one hand and a Fermi-liquid description "à la Nozières" supplemented by an argument of separation of scale on the other hand -we show that they both lead to (essentially) the same quasi-particle spectra, providing in this way a strong indication that they both give the correct physics of this regime.

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.

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.