Wilson and Kadowaki-Woods Ratios in Heavy Fermions

Recently we have shown that a one-parameter scaling, $T_{coh}$, describes the physical behavior of several heavy fermions in a region of their phase diagram. In this paper we fully characterize this region, obtaining the uniform susceptibility, the resistivity and the specific heat in terms of the coherence temperature $T_{coh}$. This allows for an explicit evaluation of the Wilson and the Kadowaki-Woods ratios in this regime. These quantities turn out to be independent of the distance $|\delta|$ to the quantum critical point (QCP). The theory of the one-parameter scaling corresponds to a local interacting model. Although spatial correlations are irrelevant in this case, time fluctuations are critically correlated as a consequence of the quantum character of the transition.Comment: 6 pages, 1 figure, to be published in Eur.Phys.J.

Dimensional Crossover in Heavy Fermions

Recently we have shown that a one-parameter scaling, the Coherence Temperature, describes the physical behavior of several heavy fermions in a region of their phase diagram. In this paper we fully characterize this region, obtaining the uniform susceptibility, the resistivity and the specific heat. This allows for an explicit evaluation of the Wilson and the Kadowaki-Woods ratios in this regime. These quantities turn out to be independent of the distance to the critical point. The theory of the one-parameter scaling corresponds to a zero dimensional approach. Although spatial correlations are irrelevant in this case, time fluctuations are critically correlated and the quantum hyperscaling relation is satisfied for $d=0$. The crossover from $d=0$ to $d=3$ is smooth. It occurs at a lenght scale which is inversely related to the stiffness of the lifetime of the spin fluctuations.Comment: 4 pages, revtex, no figures, submitted to Physical Review

Thermodynamic quantum critical behavior of the Kondo necklace model

We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions $d$ using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in $d\geq 3$ there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In 2-d, long range magnetic order occurs only at T=0. The line of Neel transitions for $d>2$ varies with the distance to the quantum critical point QCP $|g|$ as, $T_N \propto |g|^{\psi}$ where the shift exponent $\psi=1/(d-1)$. In the paramagnetic side of the phase diagram, the spin gap behaves as $\Delta\approx \sqrt{|g|}$ for $d \ge 3$ consistent with the value $z=1$ found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for $k_BT\gg\Delta$ and along the non-Fermi liquid trajectory. For $k_BT \ll\Delta$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.Comment: Submitted to PR