Heat transport and spin-charge separation in the normal state of high temperature superconductors

Hill et al. have recently measured both the thermal and charge conductivities in the normal state of a high temperature superconductor. Based on the vanishing of the Wiedemann-Franz ratio in the extrapolated zero temperature limit, they conclude that the charge carriers in this material are not fermionic. Here I make a simple observation that the prefactor in the temperature dependence of the measured thermal conductivity is unusually large, corresponding to an extremely small energy scale $T_0 \approx 0.15$ K. I argue that $T_0$ should be interpreted as a collective scale. Based on model-independent considerations, I also argue that the experiment leads to two possibilities: 1) The charge-carrying excitations are non-fermionic. And much of the heat current is in fact carried by distinctive charge-neutral excitations; 2) The charge-carrying excitations are fermionic, but a subtle ordering transition occurs at $T_0$.Comment: 3 pages, 1 figur

Destruction of the Kondo effect in a multi-channel Bose-Fermi Kondo model

We consider the SU(N) x SU(kappa N) generalization of the spin-isotropic Bose-Fermi Kondo model in the limit of large N. There are three fixed points corresponding to a multi-channel non-Fermi liquid phase, a local spin-liquid phase, and a Kondo-destroying quantum critical point (QCP). We show that the QCP has strong similarities with its counterpart in the single-channel model, even though the Kondo phase is very different from the latter. We also discuss the evolution of the dynamical scaling properties away from the QCP.Comment: 2 papes, 2 figures, submittet to SCES'0

Multi-Scale Link Prediction

The automated analysis of social networks has become an important problem due to the proliferation of social networks, such as LiveJournal, Flickr and Facebook. The scale of these social networks is massive and continues to grow rapidly. An important problem in social network analysis is proximity estimation that infers the closeness of different users. Link prediction, in turn, is an important application of proximity estimation. However, many methods for computing proximity measures have high computational complexity and are thus prohibitive for large-scale link prediction problems. One way to address this problem is to estimate proximity measures via low-rank approximation. However, a single low-rank approximation may not be sufficient to represent the behavior of the entire network. In this paper, we propose Multi-Scale Link Prediction (MSLP), a framework for link prediction, which can handle massive networks. The basis idea of MSLP is to construct low rank approximations of the network at multiple scales in an efficient manner. Based on this approach, MSLP combines predictions at multiple scales to make robust and accurate predictions. Experimental results on real-life datasets with more than a million nodes show the superior performance and scalability of our method.Comment: 20 pages, 10 figure

A Divide-and-Conquer Solver for Kernel Support Vector Machines

The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel divide-and-conquer solver for kernel SVMs (DC-SVM). In the division step, we partition the kernel SVM problem into smaller subproblems by clustering the data, so that each subproblem can be solved independently and efficiently. We show theoretically that the support vectors identified by the subproblem solution are likely to be support vectors of the entire kernel SVM problem, provided that the problem is partitioned appropriately by kernel clustering. In the conquer step, the local solutions from the subproblems are used to initialize a global coordinate descent solver, which converges quickly as suggested by our analysis. By extending this idea, we develop a multilevel Divide-and-Conquer SVM algorithm with adaptive clustering and early prediction strategy, which outperforms state-of-the-art methods in terms of training speed, testing accuracy, and memory usage. As an example, on the covtype dataset with half-a-million samples, DC-SVM is 7 times faster than LIBSVM in obtaining the exact SVM solution (to within $10^{-6}$ relative error) which achieves 96.15% prediction accuracy. Moreover, with our proposed early prediction strategy, DC-SVM achieves about 96% accuracy in only 12 minutes, which is more than 100 times faster than LIBSVM

Fermi Surface and Magnetism in the Kondo lattice: A Continuum Field Theory Approach

We consider the Fermi surface inside the antiferromagnetic ordered region of a Kondo lattice system in an arbitrary dimension higher than one. We establish the existence of ${\rm AF_S}$, an antiferromagnetic phase whose Fermi surface is ``small,'' in the sense that the local moments do not participate in the Fermi-surface formation. This is in contrast to the ``large'' Fermi surface that is typically assumed for heavy fermion metals. We extend our earlier work to the case that the Fermi surface of the conduction electrons intersects the antiferromagnetic Brillouin zone boundary. Our results provide a new perspective on local quantum criticality. In addition, our results imply that, for the ${\rm AF_S}$ phase, it is important to keep track of the dynamical screening processes; we suggest that this effect is not captured in a recent variational Monte-Carlo study of the Kondo lattice.Comment: 2 pages, 1 embedded eps figure, proceedings of SCES'0

Quantum Criticality and the Kondo Lattice

Quantum phase transitions (QPTs) arise as a result of competing interactions in a quantum many-body system. Kondo lattice models, containing a lattice of localized magnetic moments and a band of conduction electrons, naturally feature such competing interactions. A Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction among the local moments promotes magnetic ordering. However, a Kondo exchange interaction between the local moments and conduction electrons favors the Kondo-screened singlet ground state. This chapter summarizes the basic physics of QPTs in antiferromagnetic Kondo lattice systems. Two types of quantum critical points (QCPs) are considered. Spin-density-wave quantum criticality occurs at a conventional type of QCP, which invokes only the fluctuations of the antiferromagnetic order parameter. Local quantum criticality describes a new type of QCP, which goes beyond the Landau paradigm and involves a breakdown of the Kondo effect. This critical Kondo breakdown effect leads to non-Fermi liquid electronic excitations, which are part of the critical excitation spectrum and are in addition to the fluctuations of the magnetic order parameter. Across such a QCP, there is a sudden collapse of the Fermi surface from large to small. I close with a brief summary of relevant experiments, and outline a number of outstanding issues, including the global phase diagram.Comment: 27 pages, 6 figures; Chapter of the book "Understanding Quantum Phase Transitions", ed. Lincoln D. Carr (CRC Press/Taylor & Francis, Boca Raton, 2010