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.