Anderson-Yuval approach to the multichannel Kondo problem

We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant level model. Limiting cases in which the equivalent resonant level model is solvable are identified. The solution correctly captures the properties of the two channel Kondo model, and also allows an analytic description of the cross-over from the non Fermi liquid to the Fermi liquid behavior caused by the channel anisotropy.Comment: 23 pages, ReVTeX, 4 figures av. on reques

Multi-Channel Kondo Necklace

A multi--channel generalization of Doniach's Kondo necklace model is formulated, and its phase diagram studied in the mean--field approximation. Our intention is to introduce the possible simplest model which displays some of the features expected from the overscreened Kondo lattice. The $N$ conduction electron channels are represented by $N$ sets of pseudospins \vt_{j}, $j=1, ... , N$, which are all antiferromagnetically coupled to a periodic array of |\vs|=1/2 spins. Exploiting permutation symmetry in the channel index $j$ allows us to write down the self--consistency equation for general $N$. For $N>2$, we find that the critical temperature is rising with increasing Kondo interaction; we interpret this effect by pointing out that the Kondo coupling creates the composite pseudospin objects which undergo an ordering transition. The relevance of our findings to the underlying fermionic multi--channel problem is discussed.Comment: 29 pages (2 figures upon request from [email protected]), LATEX, submitted for publicatio

Anomalous heavy-fermion and ordered states in the filled skutterudite PrFe4P12

Specific heat and magnetization measurements have been performed on high-quality single crystals of filled-skutterudite PrFe_4P_{12} in order to study the high-field heavy-fermion state (HFS) and low-field ordered state (ODS). From a broad hump observed in C/T vs T in HFS for magnetic fields applied along the direction, the Kondo temperature of ~ 9 K and the existence of ferromagnetic Pr-Pr interactions are deduced. The {141}-Pr nuclear Schottky contribution, which works as a highly-sensitive on-site probe for the Pr magnetic moment, sets an upper bound for the ordered moment as ~ 0.03 \mu_B/Pr-ion. This fact strongly indicates that the primary order parameter in the ODS is nonmagnetic and most probably of quadrupolar origin, combined with other experimental facts. Significantly suppressed heavy-fermion behavior in the ODS suggests a possibility that the quadrupolar degrees of freedom is essential for the heavy quasiparticle band formation in the HFS. Possible crystalline-electric-field level schemes estimated from the anisotropy in the magnetization are consistent with this conjecture.Comment: 7 pages and 7 figures. Accepted for publication in Phys. Rev.

Local fluctuations in quantum critical metals

We show that spatially local, yet low-energy, fluctuations can play an essential role in the physics of strongly correlated electron systems tuned to a quantum critical point. A detailed microscopic analysis of the Kondo lattice model is carried out within an extended dynamical mean-field approach. The correlation functions for the lattice model are calculated through a self-consistent Bose-Fermi Kondo problem, in which a local moment is coupled both to a fermionic bath and to a bosonic bath (a fluctuating magnetic field). A renormalization-group treatment of this impurity problem--perturbative in $\epsilon=1-\gamma$, where $\gamma$ is an exponent characterizing the spectrum of the bosonic bath--shows that competition between the two couplings can drive the local-moment fluctuations critical. As a result, two distinct types of quantum critical point emerge in the Kondo lattice, one being of the usual spin-density-wave type, the other ``locally critical.'' Near the locally critical point, the dynamical spin susceptibility exhibits $\omega/T$ scaling with a fractional exponent. While the spin-density-wave critical point is Gaussian, the locally critical point is an interacting fixed point at which long-wavelength and spatially local critical modes coexist. A Ginzburg-Landau description for the locally critical point is discussed. It is argued that these results are robust, that local criticality provides a natural description of the quantum critical behavior seen in a number of heavy-fermion metals, and that this picture may also be relevant to other strongly correlated metals.Comment: 20 pages, 12 figures; typos in figure 3 and in the main text corrected, version as publishe

Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment

In this paper, we review theoretical and experimental research on rare region effects at quantum phase transitions in disordered itinerant electron systems. After summarizing a few basic concepts about phase transitions in the presence of quenched randomness, we introduce the idea of rare regions and discuss their importance. We then analyze in detail the different phenomena that can arise at magnetic quantum phase transitions in disordered metals, including quantum Griffiths singularities, smeared phase transitions, and cluster-glass formation. For each scenario, we discuss the resulting phase diagram and summarize the behavior of various observables. We then review several recent experiments that provide examples of these rare region phenomena. We conclude by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative Ising chain fixed, references added, v3: final version as publishe

Thresholds for adding degraded tropical forest to the conservation estate

Logged and disturbed forests are often viewed as degraded and depauperate environments compared with primary forest. However, they are dynamic ecosystems1 that provide refugia for large amounts of biodiversity2,3, so we cannot afford to underestimate their conservation value4. Here we present empirically defined thresholds for categorizing the conservation value of logged forests, using one of the most comprehensive assessments of taxon responses to habitat degradation in any tropical forest environment. We analysed the impact of logging intensity on the individual occurrence patterns of 1,681 taxa belonging to 86 taxonomic orders and 126 functional groups in Sabah, Malaysia. Our results demonstrate the existence of two conservation-relevant thresholds. First, lightly logged forests (68%) of their biomass removed, and these are likely to require more expensive measures to recover their biodiversity value. Overall, our data confirm that primary forests are irreplaceable5, but they also reinforce the message that logged forests retain considerable conservation value that should not be overlooked