It is shown that the large-N approach yields two energy scales for the Kondo lattice model. The single-impurity Kondo temperature, TK, signals the onset of local singlet formation, while Fermi liquid coherence sets in only below a lower scale, T ⋆ . At low conduction electron density nc ("exhaustion" limit) , the ratio T ⋆ /TK is much smaller than unity, and is shown to depend only on nc and not on the Kondo coupling. The physical meaning of these two scales is demonstrated by computing several quantities as a function of nc and temperature.

We study the competition between the Kondo effect and frustrating exchange interactions in a Kondo-lattice model within a large-N dynamical mean-field theory. We find a T = 0 phase transition between a heavy Fermi-liquid and a spin-liquid for a critical value of the exchange Jc = T 0 K , the single-impurity Kondo temperature. Close to the critical point, the Fermi liquid coherence scale T ⋆ is strongly reduced and the effective mass strongly enhanced. The regime T > T ⋆ is characterized by spin-liquid magnetic correlations and non-Fermi-liquid properties. It is suggested that magnetic frustration is a general mechanism which is essential to explain the large effective mass of some metallic compounds such as LiV2O4.

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

We argue that near a Kondo breakdown critical point, a spin liquid with spatial modulations can form. Unlike its uniform counterpart, we find that this occurs via a second order phase transition. The amount of entropy quenched when ordering is of the same magnitude as for an antiferromagnet. Moreover, the two states are competitive, and at low temperatures are separated by a first order phase transition. The modulated spin liquid we find breaks Z4 symmetry, as recently seen in the hidden order phase of URu2Si2. Based on this, we suggest that the modulated spin liquid is a viable candidate for this unique phase of matter.

The interplay between the Kondo effect and disorder is studied. This is done by applying a matrix coherent potential approximation (CPA) and treating the Kondo interaction on a mean-field level. The resulting equations are shown to agree with those derived by the dynamical mean-field method (DMFT). By applying the formalism to a Bethe tree structure with infinite coordination the effect of diagonal and off-diagonal disorder are studied. Special attention is paid to the behavior of the Kondo-and the Fermi liquid temperature as function of disorder and concentration of the Kondo ions. The non monotonous dependence of these quantities is discussed.

The thermodynamic and transport properties of intermetallic compounds with Ce, Eu, and Yb ions are discussed using the periodic Anderson model with an infinite correlation between f electrons. At high temperatures, these systems exhibit typical features that can be understood in terms of a single impurity Anderson or Kondo model with Kondo scale TK . At low temperatures, the normal state is governed by the Fermi liquid (FL) laws with characteristic energy scale T0. The slave boson solution of the periodic model shows that T0 and TK depend not only on the degeneracy and the splitting of the f states, the number of c and f electrons, and their coupling, but also on the shape of the conduction electrons density of states (c DOS) in the vicinity of the chemical potential.We show that the details of the band structure determine the ratio T0/TK and that the crossover between the high-and low-temperature regimes in ordered compounds is system-dependent. A sharp peak in the c DOS yields T0 ≪TK and explains the 'slow crossover' observed in YbAl3 or YbMgCu4. A minimum in the c DOS yields T0 ≫TK , which leads to the abrupt transition between the high-and low-temperature regimes in YbInCu4. In the case of CeCu2Ge2 and CeCu2Si2, where T0 ≃ TK , the slave boson solution explains the pressure experiments which reveal sharp peaks in the T 2 coefficient of the electrical resistance, A = ρ(T )/T 2 , and the residual resistance. These peaks are due to the change in the degeneracy of the f states induced by the applied pressure.The FL laws explain also the correlation between the specific heat coefficient γ = CV /T and the slope of the thermopower α(T )/T , or between γ and the A coefficient of the resistivity. For N -fold degenerate model, the FL laws explain the deviations from universal value of the Kadowaki-Woods ratio, RKW = A/γ 2 , and the ratio q = lim {T →0} α/γT . The renormalization of transport coefficients can invalidate the Wiedemann-Franz law and lead to an enhancement of the thermoelectric figure-ofmerit. We show that the low-temperature response of the periodic Anderson model can be enhanced (or reduced) with respect to the predictions based on the single-impurity models that give the same high-temperature behavior.

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We study the low-energy states of Kondo alloys as a function of the magnetic impurity concentration per site x and the conduction electron average site occupation n(c). Using two complementary approaches, the mean-field coherent potential approximation and the strong-coupling limit, we identify and characterize two different Fermi-liquid regimes. We propose that both regimes are separated by a Lifshitz transition at x=n(c). Indeed, we predict a discontinuity of the number of quasiparticles that are enclosed in the Fermi surface. This feature could provide a scenario for the non-Fermi liquid properties that were recently observed in Kondo alloy systems around x=n(c).