Nonlinear Sigma Model Analysis of the AFM Phase Transition of the Kondo Lattice

We have studied the antiferromagnetic quantum phase transition of a 2D Kondo-Heisenberg square lattice using the non-linear sigma model. A renormalization group analysis of the competing Kondo -- RKKY interaction was carried out to 1-loop order in the $\epsilon$ expansion, and a new quantum critical point is found, dominated by Kondo fluctuations. In addition, the spin-wave velocity scales logarithmically near the new QCP, i.e breakdown of hydrodynamic behavior. The results allow us to propose a new phase diagram near the AFM fixed point of this 2D Kondo lattice model.Comment: 4 pages, 4 figure

A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known. Further, the hierarchical algorithm can be used to recover the $d$ largest singular values and left singular vectors with bounded error. We also show that the proposed method is stable with respect to roundoff errors or corruption of the original matrix entries. Numerical experiments validate the proposed algorithms and parallel cost analysis